I've sold old ride on mowers Norm with a working solenoid and switch but no engine for less than the eBay price for solenoid and switch.
buy from China and get free post.
Yes you could also use the plastic switch or the Massey Ferguson . one but the tractor one is about $40. The plastic switch needs to be of good quality as some are low amps ,Look for a clearly stated DC rating, for example “continuous 100–200 A, cranking 300–500 A at 12 V”; using it to crank a mower starter is only sensible if the cranking rating comfortably exceeds the mower’s peak draw (often around 100–150 A