I have had steroid injections in both wrists and was back to work afterwards, teaching student nurses. The splints keep your wrists in a fixed position but you can still use your hands, although it makes typing very difficult so I stayed away from that for 48hrs. The reason for the splints is to to stop you using the wrists and hands too much, this enables the steroids to stay where they are required for longer. If you were to use the wrists and hands a great deal after the injection, this would increase the blood flow to the wrists and hands, which washes the steroids away from that area much more quickly.
They will probably ask you to use your hands as little as possible for up to 48 hours afterwards, but giving injections and eating etc is possible. You can also bathe yourself and do all the other personal things.
Just remember steroids raise the BS so it is likely you could have some spikes of high BS after the procedure. It should not persist for too long and you should ask you diabetes nurse how to deal with that if it concerns you. However my BS has usually returned to normal after 72 hours at the most.
Liz