ROBERT - Welcome to the best CC forum on the internet. 105 is a good tractor, 12 HP K301 Kohler in it only makes it better! There's places/companies that specialize in supplying repower kits for garden tractors but to be quite honest I don't know if anyone makes a kit for an old narrow frame Cub Cadet. My Dad bought a brand new Kohler Magnum 12 engine to replace the worn out K301 12 HP engine in a 129 CC He had and it turned into a VERY expensive project, and it was still the "old fashioned flathead design". Cub Cadets take a special crankshaft and special oil pan so that ALL 1-cyl. Cub Cadet engines are interchangable, from 7 HP to 16 HP.
If by "Modern Engine" You mean OHV or OHC I'm sure something can be made to fit with enough cutting, welding, etc. BUT, by the time You find & buy the engine, modify everything required to make it work the Dollars add up fast! And most of the new engines are almost all aluminum, don't have as much lugging power as the K-series Kohlers, and they aren't rebuildable.
There's been a lot of discussion here lately about rebuilding engines. To replace the piston, rings, connecting rod, exh. valve, all new seals & gaskets, rebuild the carb, new plug, points, condensor, bore the cylinder oversize, grind the rod journal on the crankshaft undersize to make it round and straight again, parts and machine work should only cost between $400-$500 with all Kohler OEM parts. Quality aftermarket parts like STENS will reduce that a bit.
If You can remove and reinstall the engine and disassemble/reassemble the engine yourself that is Your cheapest option. If You don't have the time, tools, or experience to assemble the Kohler a local small engine shop would add several hundred Dollars to the cost.
There are complete rebuilt Kohler K301 engines on E-bay from time-to-time. But like all things on E-Bay, Buyer Beware!
Choice all depends on how much work You want to do to replace the engine with something of a newer Modern design, and how much Money is TOO Much.