I want to install a tremelo / whammy bar on my guitar, but it has no cavity, so I'm aiming for a pressure / roller-type that can simply be screwed / mounted to the front of the guitar without the need for a cavity....

...does anyone know of any cheap alternatives to a bigsby (this is the only type of tremelo I am familiar with, unfortunatly)

Cheap not really. If you want a good 1 that will stay in tune then you gonna need to spend a few bucks. Are you looking to do any more than vibrato? If so then your gonna want an actual wammy. Anything like a bigsby, maestro, etc only do about 1/2 step either way.