Please go and see a doctor about this. You may have a medical condition (endometriosis or other) that makes penetrative sex extremely painful.
That does not mean you cannot enjoy sex, but it is important to get clarity on this before you do anything else.
Or Greenland could just sue them in the US, either in Texas or New York, and, at the same time, ban their supply ship from Greenland waters, and request (through Denmark) NATO assistance in order to prevent their ship or aircraft from landing in Greenland.
If any ship or aircraft ever lands, seize the contents and fine the company large sums of money for illegal drilling and operating in a sovereign country without authorization.
Locking people up for a couple of weeks before expelling them also could be considered.
Not everything has to be about guns. Whoever has been hired by this company to provide security will probably quickly understand that area outnumbered by Greenland law enforcement and Danish military.