Hi Denny,
Yes they should interchange. Both are 13/16" barrels, the main difference being the Seneca bbls are 27" while the Cherokee bbls are 24" (32 1:30", 36 1:48", 45 1:48").
However there is a fly in your soup IMO. While the 32 is great for squirrels, the 36 is not really enough for deer except up very close maybe. A 45 is a much better choice for your grandson's deer rifle, especially since his ability to make well placed shots will only come with time and experience. Sure anything might kill a deer cleanly, but IMO you are under gunning him for deer with a 36.
I've owned both rifles, Cherokee's in 32 and 36, and a 45 Seneca. I still own two 36 cappers, a very early CVA Squirrel and one of my TC Hawkens is a switch lock/switch barrel that has 36, 45 and 50 bbls for it. I use the 36's for predator and varmint hunting - with well placed shots they are enough for longer shots on varmints and even enough for coyotes, but IMO not enough for deer sized game. That opinion from years of shooting 36's with both PRB and maxiballs on flesh, so take it for what it's worth.
HTH,
Larry
