Would not look right. The only frame that would mate up properly is one made for a heavy barrel. Otherwise, you'll have a big, unsightly gap where the frame was made to taper down to the dimensions of the barrel.
One poster mentioned that the barrel could be machined to fit your .38 cylinder. Very true, but that will also mean that the ejector rod must be cut or replaced to match.
I had a 3" heavy barrel marked "S&W .38 Special" that turned out to have the dimensions for a .357 instead. Fortunately, my gunsmith had a .357 cylinder in his drawer and put together a great little gun. But I had a heavy-barrel frame, so the barrel diameter was not an issue. I suggest looking for the proper frame, otherwise you'll either have an obvious frankengun that you won't be able to give away or spend a lot more than its worth to make it right.