If you're afraid to poke him in the eye with the applicator put on a glove and put the medicine on your finger and gently wipe it into the eye. In larger animals I've always pulled down the bottom eyelid and stuck it there because when they blink it spreads it.
I recommend you apply and then hold on the the tortoise for a minute or two and don't let them rub it all out. If the tort is a greedy eater maybe consider offering a treat immediately after treatment to keep it distracted,