38mm = ~1.5", so look for 26 x 1.5" tires.

You can sometimes fit a 700c/29" rim with narrow tires on a frame/fork meant for wide 26" tires. (26 x 2.35" and 700c x 28mm tires have about the same 678mm diameter.) The major issue is brake reach and so this is easier when using disc or another hub brake.

But, I'd just go for 26 x 1.5" or so tires.