Centralize Oracle RMAN scripts in one server
Forget copying binaries around. I would integrate remote RMAN executions into your normal backup application/solution (i.e. filesystem backup to fire a script) for the sake of consistency. Especially scheduling of backups would be easier.

Re: "In this case parameterfile.par must exist in SRV_PROD_1". Not a problem if you dig into RMAN's own CREATE SCRIPT syntax - you can store the run{ } script inside your catalog.

Re: "rman.log will be created also on SRV_PROD_1". Not a problem if you take a look at catalog schema contests - surely there is one large table per each catalog that holds the logs anyway (I can't remember if it's ROUT or RMAN_OUT?).