Well Heck
I have two choices to pull answers from. Up first for your perusal are my Captain Schaeffer Replica 1851s. I oft shoot 'em with R & D two piece conversion cylinders. Since the guns started life as .36 Percussion, I shoot them mostly with 158Gr Swaged Wadcutters. Accuracy is pretty darn good. And I'm shooting APP so lube doesn't matter. I also shoot these guns with 105Gr .357 Truncated Cone bullets, crayon lubed, but again, with APP, lube doesn't matter. No problems at all with wadcutters.
Next up are my Open Tops. Mine are in fact "Open Tops," not conversions. The pair are also chameleons. Many Lustrum ago, I added Barrel/Cylinder combinations to the guns in .44 Special and .38 Special to compliment the original .45 Schofield chambering. When shooting the .38s, I switch back and fourth between 158Gr Wadcutters and 105Gr Truncated Cone bullets or 125Gr Truncated cone bullets. I have experienced NO problems with either smokeless (some time ago) or APP. I also shoot a Wadcutter in .45. The Specialty "Barnstormer" bullet is in truth a vary radical Hollow Base Wadcutter. Its weight is right around 130Gr. Accuracy is Excellent with either smokeless or APP.
Out of the box Swaged Wadcutters may be problematic with BP. I don't know if they carry enough lube and the lube they do carry is not compatible with BP. I would expect a goodly amount of fouling and poor long days accuracy. I must council however, that is just conjecture. I have never fired any of my HBWC with BP. Just smokeless and APP. YMMV