I can replace batteries. Who knew?
Battery had dropped to providing approximately three minutes charge.
Remarkably well - though one screw just wouldn't come out, and I had to gently break the battery. Luckily the screw then came out and the new battery went in fine.
Good lighting, and be methodical about keeping track of which screw goes where (I laid them out on two pieces of paper). Remember to connect the new battery up before replacing the outer case... :-)