I would stick a scope on it. That is what I have been running on my 44 mag for 2 years now, and having walked up on four deer that wnet into my freezer, I can't say that I found a scope to be any kind of a handicap. (any pun there unintended)
Comparing the 44 mag Handi to a pistol/revolve is a mistake. The 22" barrel behaves completely differently from a shorter handun barrel. I shoot loads of 7.3-11 grains of Blue Dot with a 200 or a 265 grain bullet and get velocities from 820-1275 fps respectively. I did not get good results with Unique, in fact, it was the most troublesome powder I used for mild loads. You will not find the Blu Dot load range I'm using in a manual, they are below starting loads, but because of the long barrel, more velocity may be gained than is wanted with book loads. Theses loads will be dirty, but accurate and cheap.
Don't reduce powders like 296/H110/AA1680. They make good full power or nearly so loads, but are not meant for use at less than 80% loading density.
Cast bullets of weights up to 265 grians do well, however the only 300 grian bullet that has shot in my barrel is the 300 (#704) of Magnus Bullet Co. The 1 in 38 twist of the NEF barrel is not suitable for such heavy bullets.
The Speer 270 Gold Dot is an exellent jacketed hunting bullet as is the Hornady 300 XTP (this bullet shoots well, it is short for it's weight) Both these do well at book maximums with H110, giving 1575 and 1525 FPS respectively from my barrel.
If you are going to shoot cast, be sure to slug your bore. Mine is .432 as are several others around here. Shooting .430 bullets is nearly a waste of time in such a barrel, my groups tightened noticably when I began using correctly sized bullets. So be sure to slug your barrel and shoot cast bullets properly sized. Keep us posted on your results.