1938
According to our friend Jacques Merot (†) reprints of the 1938 stamps were made in July / August 1949:
British: 20cg (*)
French: 10cg carmine, 20cg (*) & 1Fg orange.
(*) He said ultramarine for the F & GB 20cg but that was surely a typo.
As to the 10cg, 20cg & 1Fg stamps:
S.G. says:
GB:
10cg - orange
20cg - scarlet
1Fg - red/green
and the same for the Dues:
F:
10cg - orange
20cg - scarlet
1Fg - lake/pale green (shades)
F 1941:
10cg - orange
20cg - scarlet
1Fg - lake/pale green
and the same for the Dues:
Yvert says:
GB:
10cg - orange
20cg - red
1Fg - carmine on blue
Dues:
10cg - orange
20cg - red
1Fg - red on green
F:
10cg - orange
20cg - orange
1Fg - carmine on pale blue
F 1941:
10cg - orange
20cg - orange
1Fg - carmine on blue
Taxe:
10cg - orange
20cg - red
1Fg - red on green
Michel says:
GB:
10cg - orange
20cg - red
1Fg - red on green
Dues:
10cg - orangered
20cg - carminepink
1Fg - red on green
F:
10cg - orange
20cg - orange
1Fg - red on green
Taxe:
10cg - orangered
20cg - carminepink
1Fg - red on green
F 1941:
10cg - orange
20cg - orange
1Fg - red on green
I cannot says here what Sc*tt says as they barred me from telling information here.
As I'm red-green colourblind these catalogue informations are not very helpful for me.
"The stamps issued on June 1, 1938 were designed to overcome the exchange
difficulty in relation to stamp prices" (Hals/Collas). As there were two
currencies in use in the New Hebrides, the denominations of the stamps were
now fixed in a "gold basis" currency of francs and centimes.
Engraving: J.G. Hall
Design: adapted from a drawing of the French artist Jean Kerhor, graveur du département des colonies, (Hals Collas wrote "Jean Kehor" in error)
Recess printing: Bradbury, Wilkinson & Co., Ltd, New Malden, Surrey, England
Format: Sheets of 30 (3 x 10)
First Day: 1 June 1938 ♦ first day recorded: 1 June 1938
Perforation: 12 ♦ Watermark: Multiple Script CA / RF in sheet
This series exists with the perforated word "SPECIMEN" in the form of an arc.
See below.
The 1938 British Watermark Mult. Script CA stamps
S.-G.: 52-Yv: 112
Sc. : **-Mi: 97
S.-G.: 53-Yv: 113
Sc. : **-Mi: 98
S.-G.: 54-Yv: 114
Sc. : **-Mi: 99
S.-G.: 55-Yv: 115
Sc. : **-Mi: 100
S.-G.: 56-Yv: 116
Sc. : **-Mi: 101
S.-G.: 57-Yv: 117
Sc. : **-Mi: 102
S.-G.: 58-Yv: 118
Sc. : **-Mi: 103
S.-G.: 59-Yv: 119
Sc. : **-Mi: 104
S.-G.: 60-Yv: 120
Sc. : **-Mi: 105
S.-G.: 61-Yv: 121
Sc. : **-Mi: 106
S.-G.: 62-Yv: 122
Sc. : **-Mi: 107
S.-G.: 63-Yv: 123
Sc. : **-Mi: 108
The 1938 French Watermark RF in sheet stamps
S.-G.: F53-Yv: 100
Sc. : **-Mi: 109
S.-G.: F54-Yv: 101
Sc. : **-Mi: 110
S.-G.: F55-Yv: 102
Sc. : **-Mi: 111
S.-G.: F56-Yv: 103
Sc. : **-Mi: 112
S.-G.: F57-Yv: 104
Sc. : **-Mi: 113
S.-G.: F58-Yv: 105
Sc. : **-Mi: 114
S.-G.: F59-Yv: 106
Sc. : **-Mi: 115
S.-G.: F60-Yv: 107
Sc. : **-Mi: 116
S.-G.: F61-Yv: 108
Sc. : **-Mi: 117
S.-G.: F62-Yv: 109
Sc. : **-Mi: 118
S.-G.: F63-Yv: 110
Sc. : **-Mi: 119
S.-G.: F64-Yv: 111
Sc. : **-Mi: 120
The 1938 POSTAGE DUE - CHIFFRE TAXE stamps.
June 1, 1938 (?) : The 1938 "Postage Due" overprinting was performed by Bradbury, Wilkinson & Co., Ltd, New Malden, Surrey, England, it is smaller than the 1925 overprinting and more in the left upper corner of the stamp.
Sold mint in Vila in Jan., 1939. They are rare on cover. (Hals/Collas). The stamps exist perforated "Specimen". See below.
S.-G.: D6-Yv: T16
Sc. : **-Mi: P11
S.-G.: D7-Yv: T17
Sc. : **-Mi: P12
S.-G.: D8-Yv: T18
Sc. : **-Mi: P13
S.-G.: D9-Yv: T19
Sc. : **-Mi: P14
S.-G.: D10-Yv: T20
Sc. : **-Mi: P15
S.-G.: FD65-Yv: T11
Sc. : **-Mi: P16
S.-G.: FD66-Yv: T12
Sc. : **-Mi: P17
S.-G.: FD67-Yv: T13
Sc. : **-Mi: P18
S.-G.: FD68-Yv: T14
Sc. : **-Mi: P19
S.-G.: FD69-Yv: T15
Sc. : **-Mi: P20
Jeff Blinco found an article in the 22 February 1938 issue of "Paris-soir" about this issue:

22 February 1938
Article about the 1938 issue.
Here the name of the famous stamp artist is correctly written as "Jean Kerhor". The article tells us in February 1938 that the issue is about to leave
the print presses. It states that they are issued with nominal value in Franc gold which corresponds to 10 Francs paper for 1 Fg or about 32 shilling paper.
So the high value 10 Fg equals 100 F paper or 320 shilling paper = 16 BP or in todays value inflation included about 101 BP. This may show that these high values
were not really needed in the New Hebrides postal system.
(this part of the page added in Feb 2018)

Kerhor's design
Jean Kerhor designed the stamp with double values pence and cents. Later this was changed in Franc gold.
Jean KERHOR (Langres 2.4.1876 - Paris 6.1.1974) est le pseudonyme
d'André DUPUIS artiste graveur, dessinateur et illustrateur (arrière petit
neveu du philosophe DIDEROT).
Il arrive à NANCY en 1886 lors de la prise de fonction de son père
militaire de carrière nommé Commandant au 37è régiment d'infanterie.
Il entre à l'école des beaux arts de Nancy le 4.1.1901. Il quitte la ville en
1906 pour Paris où il entre au ministère des colonies en tant que secrétaire.
Il en devient le dessinateur attitré sous le pseudonyme de Jean Kerhor.
En 1912 il se marie avec la fille de Pierre Mahé, premier des grands
philatélistes français, créateur et conservateur de la fameuse collection
FERRARI DE LA RENOTIERE.
Il a crée des timbres pour le Togo, Cameroun, Niger, Tunisie, Tchad, Congo
belge, Nouvelles Hébrides, Guinée,Côte des Somalis.
(source: André Dupuis alias Jean Kerhor)
Information and artist design image supplied by "SeSi" - thanks!

Kerhor's design - coll. F.Petit
(new 5/2020)
And here is another copy of the Jean Kerhor design. - Signed by him at the bottom of the sheet. (Coll. Fred Petit)
The 1938 SPECIMEN stamps.
1938 British Issue Specimens. This is the "Bradbury, Wilkinson & Co. Ltd." specimen punching Type B9.
S.-G.: 52s-Yv: --
Sc. : **-Mi: --
S.-G.: 53s-Yv: --
Sc. : **-Mi: --
S.-G.: 54s-Yv: --
Sc. : **-Mi: --
S.-G.: 55s-Yv: --
Sc. : **-Mi: --
S.-G.: 56s-Yv: --
Sc. : **-Mi: --
S.-G.: 57s-Yv: --
Sc. : **-Mi: --
S.-G.: 58s-Yv: --
Sc. : **-Mi: --
S.-G.: 59s-Yv: --
Sc. : **-Mi: --
S.-G.: 60s-Yv: --
Sc. : **-Mi: --
S.-G.: 61s-Yv: --
Sc. : **-Mi: --
S.-G.: 62s-Yv: --
Sc. : **-Mi: --
S.-G.: 63s-Yv: --
Sc. : **-Mi: --
1938 French Issue Specimens.
S.-G.: F53s-Yv: --
Sc. : **-Mi: --
S.-G.: F54s-Yv: --
Sc. : **-Mi: --
S.-G.: F55s-Yv: --
Sc. : **-Mi: --
S.-G.: F56s-Yv: --
Sc. : **-Mi: --
S.-G.: F57s-Yv: --
Sc. : **-Mi: --
S.-G.: F58s-Yv: --
Sc. : **-Mi: --
S.-G.: F59s-Yv: --
Sc. : **-Mi: --
S.-G.: F60s-Yv: --
Sc. : **-Mi: --
S.-G.: F61s-Yv: --
Sc. : **-Mi: --
S.-G.: F62s-Yv: --
Sc. : **-Mi: --
S.-G.: F63s-Yv: --
Sc. : **-Mi: --
S.-G.: F64s-Yv: --
Sc. : **-Mi: --
The 1938 POSTAGE DUE - CHIFFRE TAXE SPECIMEN stamps.
S.-G.: D6s-Yv: --
Sc. : **-Mi: --
S.-G.: D7s-Yv: --
Sc. : **-Mi: --
S.-G.: D8s-Yv: --
Sc. : **-Mi: --
S.-G.: D9s-Yv: --
Sc. : **-Mi: --
S.-G.: D10s-Yv: --
Sc. : **-Mi: --
S.-G.: FD65s-Yv: --
Sc. : **-Mi: --
S.-G.: FD66s-Yv: --
Sc. : **-Mi: --
S.-G.: FD67s-Yv: --
Sc. : **-Mi: --
S.-G.: FD68s-Yv: --
Sc. : **-Mi: --
S.-G.: FD69s-Yv: --
Sc. : **-Mi: --