Is it ethical 4 a prevailing party's lawyer to compensate a mediator rather than his client paying for said costs?

No, at least in the jurisdictions in which I practice.  Attorneys are not supposed to promote litigation by paying the costs associated with it - costs are the responsibility of the client, even if the client's fee arrangement with the lawyer is a contingency.  However, it would not be unusual for the attorney to issue a check and be repaid by the client.