These were most commonly sold with straps, probably either smooth or textured leather, or pigskin. The Speedking (I believe) takes a 17mm strap. Sometimes a bracelet was offered as an option, either a riveted Oyster type (non-tapered, with straight end pieces) or bamboo or bonklip style, in the '40s.
I think you'd be fine with a brown or tan camel-grain or pigskin strap, but there's no reason you couldn't splurge and use a crocodile strap. It's whatever you like the most.
Here are some straps I've used on my vintages:
Hirsch Classic Alligator
Camel-grain leather
Hadley-Roma lizard
IW buffalo leather
NOS Gemex calf (ca. '50s)
NOS textured leather (ca. '40s-50s), not sure of the manufacturer
Barington ostrich (leg)
Here's an example of a riveted 16mm bracelet with straight end pieces (from 1954, so tapered)
