A handheld transponder would be an extremely bad idea !

Get a TRIG transponder, Mode S.
Put a stub antenna somewhere in the back pointing
down aft of the gear, with ground-plane above and inside.
Use the proper and expensive coax for the antenna;
this is not a radio shack nor shade-tree job.
Really best to get a proper radio shop to do the install.

Can't help you with a 337 but a good radio shop can.

Hope this helps,
Best Regards, Dave "YO electric"