Our mole removals are done with radiofrequency because the residual heat is much less than with laser, almost painless, and the scar is minimal. Typical procedures are done in office for less than most surgical excisions. Best to discuss this with a professional as the consequences of a bad scar will certainly be more expensive. Beware of DIY home treatments.
It is difficult to tell from your picture if the mole on your upper eyelid is flat or raised. If it is raised, it could be removed by shaving it off. If it is flat, it would need to be excised. Either method could be performed in the office and an anesthetic would be injected under it so that you would not feel anything. You should definitely see a physician to have it removed and not try removing it yourself.
Treating moles with apple cider vinegar is just plain dumb. I have seen some of the worst situations from home-care remedies. I have a patient with an 8 inch scar across her abdomen because the ACV literally ate her skin away and left a huge infection. I would absolutely not recommend putting it anywhere near your eyes. See a trained professional. The site will be numbed, a tiny instrument will be used to cut off the mole, and that will be it. A home remedy like apple cider vinegar is absolutely the worst option you have.
"This answer has been solicited without seeing this patient and
cannot be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."