Can we use a PRF as a PRP?
If the output domain is large enough so that the probability of getting a collision in the PRF is negligible, then the output of a PRP and PRF are indistinguishable. Thus, in principle, the answer is yes - you can interchange these freely (under the above condition). 

Having said that, it's unclear to me why you would want a non-invertible PRP rather than a PRF. Typically, a PRF is better for cryptographic constructions, being easier to analyze and giving better bounds, and the only time we use a PRP is when we want to invert. Maybe there is an example of a use of a PRP specifically when inversion is not needed, but I don't think I've ever seen one (and can't really think of where it would be helpful).