Using 3 gear shifter on 2-ring chaninset
Good work for using the council's eco-shop.  Its a great way to find raw parts and donor bikes for projects.

The left shifter "should" work.  but there's a risk the rider will overshift and go to the third/missing chainring.

You might get away with it by fiddling the limit screws on the FD, and set the FD so the "most slack" position on the shifter would be the missing chainring.  That way rider overshifts, the limit screw holds the FD from going too far, but the shifter simply slacks off the wire, and nothing happens.  

Give it a try and see what happens.  At worst, its a trip back to the dump in a couple weeks for another donor bike.   Or you can look for bike cooperatives in your area who may be able to help.