Using turbo trainer with solid axles
Installing quick release axles requires completely replacing the axle. It's possible but does require a few extra tools and parts to disassemble the rear hub. If you install a QR, don't forget to choose a trainer specific QR, they are strong and have tough metal nuts.

The simplest method though would be some other type of axle nut which is compatible with the turbo. Internet search for 'turbo trainer axle nuts' seems to be a good start. They have rounded metal ends and look like this: