You
can use a standard Mosin sling on an M38, but it isn't technically historically accurate. Kinda sorta.
A lot of M38's and M44's were issued with the 91/30 slings, due to production pressures and the availability of the 91/30 sling, but most were issued with a slightly shorter sling that was actually designed for them (forget the measurements off-hand).
The quick and easy way to tell the difference is a standard 91/30 sling will have a square cut leather tab for the re-enforcement of the foldover loop, and the M38/M44 slings have a v-cut. Here's a couple of pictures for clarity:
Standard 91/30 "Dog Collar" sling:
M38/M44 "Dog Collar" sling:
So...
A standard 91/30 sling will work just fine, but you'll need to cinch it up a fair bit due to the shorter distance between the two mount points. If you want to go historically accurate, you can get the proper sling on eBay, they come and go. Just keep an eye out for them once a week or so until you spot one. I paid $15 for mine plus $10 shipping, or something like that, IIRC.
Most of the dealers carry repro slings, and the leather dog-collar on them isn't 1/20th the quality of the real deal. Usually they're the NCStar slings, and the "leather" is acutally a "vaguely leather coloured leather like product of unknown origin."
Track down the real thing on eBay and you'll be happier in the long run, even if it does cost a few extra $$. Ostfront Militaria on eBay is pretty reliable, I've bought a couple of bits and bobs off him and had good luck. He doesn't have any M38 slings at the moment, but keep an eye out and his inventory changes regularly.
http://www.ebay.com/usr/ostfront.militaria