Just go for the tires, at least at first. You should have absolutely no problems mounting the 1.25's! They're made for wide mountain bike rims. (I'm running a 26MM tire on a 20MM wide 700C rim with absolutely no problem. A 1.25" is 32MM)

I'm not sure what kind of gearing etc. the cruiser has, but if it's a coaster brake, new LIGHTER wheels may be a bit more problematic. You might have to have them built, depending on how the bike is equipped.