Yes, you can do that. However, as previously mentioned, the loads will probably not print to the sights. The normal .44-40 bullet is abut 200 grains, if memory serves, and the 250 grain bullet will probably print higher.
I would think that the 250 grain bullet also defeats one of the main reasons people shoot .44-40s: reduced recoil makes them more controllable than the .45 Colt (which has trouble with light loads).
Have fun, be safe, and fully evaluate the 250s before you go into competition with them.