You could always use in-house knowledge to design something in the popular office tools including Libre Office (which really does fit the limited budget criteria).

A lot of the commerial solutions are too unwieldy to be a simple friendly user interface for remote users with infrequent application - so a bit like the human brain you would likley only use 10% of its capacity whilst paying 100% of its price / subscription.

We have a system at work the team looked at replacing only for the preferred alternative to be bought out by the existing provider so here we are plodding along with something far from ideal but no viable alternative.

Hi E Knox

I think you have largely answered your own Q.

Depending on what level of injury or not this would kick in, how many incidents would you be managing a year?

If the number is small then there is probably little benefit in having some all singing, all dancing solution that tells you that last year one person fell and twisted their ankle and one person cut their finger on a piece of paper and got first aid. 

Not enough data to get any trend analysis in periods of less than years or decades except for some underlying causes that will repeat time and time again - IFF you do effective root cause analysis.

So, probably you can get what YOU need via standard Microsoft applications. Just need some techie to do a spreadsheet or whatever, if YOU define what you want to know.

P