You can put subpanels that are larger in capacity than your feeder is. That's fine. You must put a breaker in the feeding panel sized to the ampacity of the feeder wires, so if 40A is what you need you can use #8 copper in the feeder and a 40A breaker. If you actually have 40A of load (as opposed to needing a 40A feeder), you may wish to size things up to #6 and a 60A feeder breaker.

I don't know what a "mobile mini unit" is, but I suspect you may need to install a grounding system for it as well.