I wanted to ask if I was to get laser hair removal, is it permissible to show my private parts to a female that will be carrying out the process.

Surah An-Noor, Verse 30:
قُل لِّلْمُؤْمِنِينَ يَغُضُّوا مِنْ أَبْصَارِهِمْ وَيَحْفَظُوا فُرُوجَهُمْ ذَٰلِكَ أَزْكَىٰ لَهُمْ إِنَّ اللَّهَ خَبِيرٌ بِمَا يَصْنَعُونَ

Say to the believing men that they cast down their looks and guard their private parts; that is purer for them; surely Allah is Aware of what they do (sura An Noor/30)

No it's not allowed it is haram to show one's private parts to anybody except her/his spouse.