I'd try to avoid adding the caps if possible and still safe... Are you using the transformer? Using the relay and µC as I described you don't need caps, transformers nor extra phantom source. Short pins 2 and 3, switch the old mic out, switch the new mic in, open the short circuit between pin 2 and 3. If the used preamp has good CMRR and the mics connected are DC balanced (I sincerely don't know if there's some mic out there really bad in that aspect, I expect not to) it shouldn't bang that loud. If there is a problem with one of those a transformer and a separate 48V source would help. If it's that bad this isn't enough caps and independent 48V sources.
The other option is to put a loop for the mic pre, so you can mute the output of the mic pre as well. Switching in and out the 48V for a single mic is usually loud enough that you'd like to mute the channel, you have a µC doing the switching so isn't hard to automate that. That might be the best one, still shorting pins 2 and 3 at the input but together with that (or before) muting the output. It's just one extra relay and there you can do the switching death quiet (other than present signal)
I'd still try to convince them to switch after a mic preamp, but I'd guess they it might bring them the idea to select between multiple preamps as well so I'd be afraid of asking. Knowing the selection of mics and pres that would be used could give an advantage since you would know your worst case, and you can know what freedoms/compromises you can take safely.
JS