On the other hand...
I've got two of the Winchester 1903s (I assume that's the model you're talking about). In good shape, they're quite valuable, and if the one you saw can be picked up cheaply, it might be worth a gamble.
The ammo is available on the internet for about the same price as 9mm ammo -- stiff, but not out of the question -- and both of mine are real TACK DRIVERS.
---
As Jim says, converting the gun to .22 LR is probably not realistic. And there's some question as to whether the gun will function properly after the conversion.
(The 22 autorim round is about the diameter of a 22 magnum, but about the length of a 22 Long.)