I have a handi ultra in .35 Whelen, I am shooting mostly cast 215gr gcs at up to 2600fps, no problem, but I have shot Rem. CLPSP's at 2800fps.
The stock on mine does slap my cheekbone but it is not that big a deal.
I also shoot 500gr , .45-70 's at 1650+ fps and do ok, so long as I shoot ofhand, not from the bench.
With the factory recoil pad, I really do not have a problem with any sensible loads.
Handi rifles are not that light, the .45-70 is 8.5 lb and the .35 ultra is 9.6lb with a 2.5x scope mounted.