if you'll tuck the .270 into your shoulder tightly, like it should be with any rifle or shotgun, the kick will be more manageable. the .270 is not a hard kicker, in my opinion, anyway. i've shot it in Model 77 Mark II's and in the Weatherby Vanguard off a bench, which allows 'kick' to be felt more than standing up usually -- and they are just fine. i'd expect a wooden-stocked Handi to be easy to manage as well.
My .30-06 with 'good' loads of imr 4320 and 165 gr' bullets in a relatively light Model 700 ADL syn' is easily manageable off a bench when held tight to the shoulder. I'd expect its recoil energy to be fairly higher than most .270 loads you're likely to come up with.
the .270 with a 130 gr' bullet would be my starting point for almost all of North America's big-game hunting.....regardless of rifle. that in itself helps to keep the recoil down.
take care,
ss'