You need to have the occupational first aid ticket under your belt, then once you've committed to being a volunteer they will give you further training.

To be an industrial paramedic you don't need to be doing nursing either, but to be a "real" paramedic (say, a full time, paid professional ambo), then it's a three year degree. For what I am interested in doing, no nursing degree is required. There's very little diagnosis and treatment involved, it's basically just keeping people alive long enough for the docs and nursing staff to step in.