There are IC products referred to as "power strobe" or
"load switch" meant for exactly this kind of thing. You
probably could even use something like an ACS or LVC
logic family hex inverter (all in parallel) to get a tolerable
on resistance if the powered load is reasonably low.
Or an octal bus driver, those are mighty beefy (in logic
terms anyway) with about 5 ohms series resistance
per driver, under an ohm net in parallel, and you could
choose between tristating (float the load) or 1/0 (load
is discharged when off).
Of course shuttling all the bypass capacitor charge in
and out could become more wasteful than letting the
radio sit idle (DC) depending on cycle rate. That's a
trade decision for you to make. Might look into whether
the radio has enough internal power management that
you could be happy just using its enable pin, or
something, as well.