I`ve never tried AmiModRadio, so some guessing here. Searching for different mod players in PATH is not a good idea or at least not the best as you can see. AmiModRadio uses some preferences, right? Just add there a full path to mod player (e.g. with filerequester). Then your program should check if mod player exists and if not throw out a error message. In that case the user needs to add or correct the full path.
Maybe you do the follwing already: How do you check if a mod player is already running? Most or all have an ARexx port what can be checked. Of course you can much more information about the running mod player over the port.