You will find that cleanup is easy, as long as the Buffalo Arms loads carry enough lube on the bullets.
I recently put 100 .44-40 black powder handloads through my Uberti 1860 Henry. Fifty were loaded with 28 grains of 3Fg Goex plus cornmeal filler so there wasn't air space, while the other 50 were full-power loads with 35 grains of 3Fg Goex. Bullets were home cast from an Accurate Molds 43-215C mold, which carry a lot of lube. Swiss black powder burns a lot cleaner.
To clean the rifle afterwards I used cotton flannel patches wet with a "moose milk" of Ballistol and water. About 25% Ballistol with the rest water but the mix isn't critical. What is needed is the water -- you can use a mix of soapy water, windshield wiper fluid, or Windex. Black powder solvent is water soluble.
It took about a dozen wet patches through the bore before they started coming out clean. Then a couple dry patches followed up with oil to prevent rust (I used straight Ballistol).
If you can support the rifle so that it lays horizontally with the action open and ejection port facing down, it will keep any fouling or solvent from getting into the action.
Seriously, it's easier than cleaning an AR15 or an AK.