Very few companies under, say, 100 employees have dedicated H&S officers. And to be honest, without at least a diploma level qualification and experience the chances of getting into a bigger firm are limited. You could try specialist areas like building etc though.
As for paying back the fees - this is normal, and is a usual part of an agreement. Actually - some firms will also ask you to sign a contract that you won't enter that field of work for x number of years as well. And yes, they can withhold pay.
If you're happy in the company, jump at the opportunity they're offering to gain some relevant experience for a year or two, and then look elsewhere. Sounds like they're being really supportive, and may be willing to train you to a higher level.
Just by the way : well done for continuing your education in this manner - I'm about to sit H&S exams myself so I know the time and effort involved.