My suggestion would be to carefully go over the Cox chassis. If it wasn’t abused and kept under cover it should be ok but I’ve seen some pearlers. Check for rust, pitting and wear. Make sure all the spindles and bearings are in good serviceable condition too.
If, after all of this, you’re happy, start shopping for a new (or near new) name brand engine with the right power and torque output at the right revs. Those Cox chassis, if well maintained, can outlast three good engines. There are good deals to be had on new engines if you are patient and shop around. Once you have what you need replace all the belts and, if you do all the maintenance it’ll still be going strong in 10 years.
With all the mucking about you do to get them to fit I really can’t see the value in second-hand motors with uncertainty around their maintenance on ride-ons. As for chonda motors, they can be good but there is effectively no guarantee and the prices are not so cheap that they’re throw away items. If it’s for personal use then I’d go for reliability every time.