My first thought is if you have to ask you should have a competent professional inspect the rifle and go with that person's advice whether using either of the powder choices.

If it is in good shape and has not been abused by people trying to hot rod it then it is ok for mild loads of smokeless powder. Remember the 44 is essentially bottom lever actuated rolling block. If it is not one of the heavier “schuetzen” 44s be careful.

40 Rod

Um,.....It's a rolling block only if it is one of the rare ones with the so-called "lugged hammer" that supports the breechblock on firing.   Which a .25-20 will not be.    

Load the canonical 86 grain plain base bullet to something less than 1500 fps and you'll be fine.   6.0 grains of AA#9 or Blue Dot gets you there.  (Caution:  AA #9 can be double-charged without overflowing the case, so be extra careful.)

It does make a LOT of difference whether the action locks up tightly or not.  If it's loose, it will get looser quickly.  Oversize link pins are usually the answer.  A .1965 decimal reamer and pins made from 5mm dowels usually works.  The action may be a tad stiff at first, because that combination gives you a  nominal .0003 interference fit, but it'll stay tight longer that way.   If the link pin holes are really trashed, you might have to go up to 7/32".  

McMaster has both the reamer and the dowels.  
Dowels:  Item # 91595A352
Reamer: Item # 8803A378