If the finish work is questionable, I imagine what is underneath might be the same...or worse.
I would at least take up the tile on the floor and on the curb. The curb is one area that is usually neglected when it comes to waterproofing, and what you see under there will give you an idea of what the rest of the shower looks like.
Actually, after 20 years, a conventional shower is probably due for a rebuild anyway. If it still drains properly and you can get by replacing only the floor tile, that's certainly a cost-saving option.
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The top ten reasons to procrastinate:
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