Is it possible for me to remove a skin tag wart on eye myself?

Yes, but not smart!: Sure-if you are very dexterous and don't mind the pain ; risk of infection, bleeding and the unknown. What you are describing is likely a true fibro-epithelioma (skin tag) or could be a filiform wart or even a skin cancer. You are best be treated in the doctors office where a sterile field, anesthesia and appropriate pathology and followup can be performed. Ps-that solution on tv-not great idea!

I would not: I would see a doctor and let them check and treat you, if you need treated.