Damage due to belt breaking depends on the engine being “interference” or not, not the cover. Just google your engine or look on the gates belt website, there is a PDF file with most engines listed and the ones that are interference have * next to it. An interference engine would have the valves and the piston contact each other if the belt is snapped and they are free spinning.
As far as who is best to do the job, get some quotes and references, I do not see an independent shop having much trouble with this.
The water pump is usually changed with this job just because it does not cost much in parts-the labor is rather high, so if your pump decides to say goodbye in another year, then you are on the hook for pretty much the same amount of $$ san the belt price.