Depending on the derailleur, you may be able to get 10 speed shifters to work if you also swap the cassette to 10 speed. The derailleur may have enough range to sweep the whole cassette. I've had luck using a deore lx 9-speed derailleur with 10-speed shifters and cassette. Worst case for the rear is that you'll need a new rear derailleur.

You may also have issues setting up the front. You probably want to have the shifter use the top 2 indexing positions. The tricky part is going to be getting the tension set right and fine tuning the indexing. You'll probably have to play with it a bit, adding an inline cable adjuster (jagwire makes these) might help with this process. You'll also need to make sure you get the limits dialed in on the limit screws so that it doesn't overshoot on the bottom end. It's totally doable though.

Depending on the derailleur, you may be able to get 10 speed shifters to work if you also swap the cassette to 10 speed. The derailleur may have enough range to sweep the whole cassette. I've had luck using a deore lx 9-speed derailleur with 10-speed shifters and cassette. Worst case for the rear is that you'll need a new rear derailleur.