A lot depends upon what you’re doing. Generally, yes, a workshop will have sharp stuff. But not everyone will have potential for burns.
In the realm of sticking plasters, I really wouldn’t worry too much; in the event that one is needed, you’ve time to stop everything, walk back to the kitchen for a cuppa and to sort yourself out properly. Or more likely, tape it up with masking tape and carry on.
The things which beg further thought are those potential injuries that demand more urgent attention. So to go back to the burns example, I’d want a clean water source, to cool a thermal injury or to wash a chemical one. And in the case of electrical burn, a means to isolate the power.
As for cuts (by which I mean serious ones, where the priority is stemming the bleeding), keep it simple with a quantity of bandages.
Advice on tourniquets has changed over the years. Once fitted (the time should be noted), they will be painful, but should not be removed until you are in hospital.
However, were a tourniquet called for, there is likely to be a risk of shock (not the type from receiving bad news!), which brings me back to someone’s earlier point of the need to be able to summons help! A first aider’s first act should be to call for help, be that of a friend, colleague, passer by or the emergency services.
