Even though the wife bought this just in her name & it is only her name on the loan, the husband will still have to sign off on the Short Sale because it's now considered community property. That alone does NOT affect his credit.
The thing I would be concerned with is that they are married & they are probably on Joint checking / savings accounts & even when credit reports are pulled, because of the marriage, reporting is "mixed".
My suggestion to do right now: Prior to even listing the home for the inevitable short sale, talk to a lender, an experienced lender & have them do a pre-qualification / pre-approval NOW, just for the husband, be HONEST with them & let them know about the wife being on this soon to be "shorted" loan & see what they say.
Better to know this sooner than later.
If you would like a referral to a good lender who is a direct funder & has been in the business for 30yrs, just let me know.