KEVIN P. - If I understand correctly what You broke, that actually attaches UNDER the big hex nut & flat washer that holds Your flywheel onto the tapered end of the crankshaft. All that actually drives it is a short little 1/4" dia dowel pin and the friction of the big nut & washer.
Sorry to say the engine really has to come out, BUT since it's a 10 HP, the bottom of the oil pan should be flat. Remove the four 3/8" capscrews from the underside of the frame that fasten the engine in, back the PTO clutch linkage ALL the way out so one end comes out of the turnbuckle that adjusts the clutch, slide the engine forward, then lift the engine up and slide a piece of 1/2" to 3/4" plywood under the engine to hold it up above the top of the frame. I don't think You'll have to remove the choke & throttle linkage, leave the hood & grill on. Use either an impact wrench or a socket & ratchet to remove the big hex nut, I think it's 15/16" if I remember right. If You use the socket/ratchet You may have to hit the handle with a hammer to break the nut loose. The grass screen is held onto the diecast driver/pulley with four little hex head screws. If Your screen isn't torn up too bad You may just need the driver with dowel pin. Don't mess with the flywheel, just install the driver, thick flat washer, nut, maybe a drop of Lock-Tite, and You should tighten that nut with a torque wrench. Then install Your three-pin clutch driver, anti-rattle springs go on the pins before You slide the engine back into position. Set the engine back down into the frame, slide it back, install the four 3/8" capscrrews that hold the engine in...reattach the PTO clutch rod to the turnbuckle & adjust.
With any kind of luck You should be able to accomplish that repair in an hour or two.