Not that I believe you but...

If you can keep hitting until you bust the only meaningful deviation is to double more hands than you would have, then play them out using basic strategy if you hit a stiff or soft hand.

There are a number of BJ calculators online that give the EV of a given strategy option vs a given upcard. Any hand that is +EV as a hit (meaning the hand actually has value, not less -EV than standing) becomes a double. That's it.

If you can only hit once I'd just use the above strategy except maybe if the original EV of hitting is barely above 0.