Yes it will handle +P with no problem.

Just my opinion, and worth what you paid for it but since the gun is relatively rare, I would stick with standard .38 for range use, and then maybe a few +P's here and there.......and then keep it loaded with +P for defense. Not that it can't "handle" +P, but hotter ammo will add more "stress" to the gun over time,more forcing cone erosion, more endshake, etc. but I honestly doubt it would matter much unless you fire many 1,000's of rounds of +P through it.

If you are not a collector, you could sell that early 64 for a decent profit, get a later Model 64 Heavy Barrel and have some change left over for ammo and then some. Decent used 64's are about $200-300 for a security trade in, maybe $400 for a nicer one.......the early 64's can go for upwards of $500-600.....Lots of S&W collectors would be glad to have that early 64, and many are probably secretly cringing at the idea of one being used as a shooter. I would say load it with .38's and fire away, if you take care of it, it will last forever.