Looks like mucho Dolares :-)
Nope, can be done, you just have to make sure that it bridges any gaps that might be there when RF drops out for a moment if that's a concern. Also, keep in mind that rectifying means the switch will be "in limbo" until the power supply comes up (which will not be instant). You don't want to fry the PIN diodes in there during the first millisecond of so. Best to talk to the manufacturer about any "grace periods" here but chances are they won't know because they may have never tested that.
It is possibly to make switchers that can bring the output up to spec voltage in under 200 microseconds. But that wouldn't help much if that's enough to make the PIN diodes in your switch module go phssst ... *PHUT* because they saw RF power before it was switched to a defined state.
At gigahertzes I'd forget transformers. Yeah, you could do stripline/microstrip stuff but that gets old when your frequency range is wide. You could just rectify and then use two buck converters to get from your 40-50V down to 5V and 15V. Use some automotive rated switcher chip that is ok up to 100V. Linear Technology etc. Rectifier diodes for that voltage level and GHz-range is another matter.
Make sure nothing "spills back" into the RF. When the load is varying you will effectively AM-modulate your RF source via load changes. So think about whether that could cause some grief and how much AM you can tolerate. If the switch control draws fairly constant current that can be ok but there may be a load glitch when it swings.
You need very small ceramic RF caps and they need to be rated 100V. 63V would be a white-knuckle ride. Haven't looked but try Johanson. If you get stuck on the caps post again. Then, if you fear load changes or RF drop-outs, follow that with a choke and an electrolytic.
I think this can be done.