The light cowboy loads, with cast lead bullets shouldn't be a problem in your 1893. You might check Old West Scrounger, if you really want to shoot black powder.
I load and shoot smokeless in mine regularly, but only in reduced loads.
Early Marlin catalogs state that the Grade "B" rifles were okay to use with "Low Pressure" smokeless catridges, IE: smokeless loads that duplicated black powder velocities. There were "High Power Smokeless" cartridges for both the 32-40 and 38-55. These were discouraged for use in the Grade "B". Smokeless handloads can be assembled that produce low pressures and fine accuracy. I used smokeless exclusively in both of my Trapdoor Springfields. I fired hundreds of low to mid powered loads through them with no ill effects. My Grade "B" 32-40 is digesting 6.6 grains of Unique with a hardcast 170 grain Meister bullet with ease.