Disabling back-pedal brake I have a bike with the so-called back-pedal brake, but since it's for someone who's learning I think that it's more an obstacle than an advantage.

Since the bike also has hand-actioned brakes, can I remove the back-pedal braking effect without replacing the wheel?
What you most likely have is an old-fashioned coaster brake, along with a hand brake.  In reality the coaster brake is probably more "natural" for someone learning -- the hand brake is mostly an affectation designed to make the bike appeal more to boys (of all ages).

But it is possible to disassemble the rear hub and disable the brake in most cases.  There are 3-4 different mechanisms used, so it's impossible to give you detailed instructions, but it would be apparent to anyone with sufficient mechanical aptitude.  (But note that the rear hub, in addition to being very greasy inside, contains lots of little parts, and reassembly requires some skill.)