Will tagging a protease with HlyA for secretion inactivate the protease?
Unless someone has actually done this specific fusion and reported on the activity, this question won't have an answer. I can't find anything about proline aminopeptidase fusions, but enzyme-HlyA fusions have been done that retained activity similar to the wild-type protein (examples: cutinase, β-lactamase). Your fusion might work fine or folding might be disrupted after secretion (either by the tag itself or by the absence of chaperones, if required). In other words, you need to try it yourself. 

Bacillus subtilis is commonly used for secretory protein production and may present another/better option.