Ay mama, totally get your worry, waiting around na lang with days running out is stressful talaga! So from what I've heard, a lot of mums got their warts removed with local anesthesia lang and it went fine, lalo na since yours are on the outside part pa lang. The thing is, most OBs do refer to infectious disease specialists para sa procedure kasi they want everything safe for both you and baby, plus they use topical or local anesthesia which shouldn't be an issue for delivery healing. My neighbour actually had her warts treated at around 36 weeks with just local anesthesia at a private clinic, and she was able to deliver vaginally a few weeks later with no complications, wounds healed nicely pa.
That said, the timing worry is real, wound healing takes a couple weeks, so you might want to ask your OB or the ID doctor straight up kung kaya pa ba gawin ito at 35 weeks, or kung mas safe mag-wait after delivery nalang (some mums do that too, no judgment). If you're feeling rushed or uncomfortable with the timeline your current OB is giving, getting a second opinion isn't bad, most doctors are cool about it! Definitely ask your OB or the specialist kung realistic ang healing timeline before delivery, para you can peace of mind better. Sending you all the good vibes, mama!