Redoing Caulk around pool.

I would only leave it in place and forego replacement as a last resort. Have you tried using a painter's 5-way tool to remove it? Great little tools for use as scraper/pick for jobs like this. (Note, you get what you pay for with these.)

Of course your site conditions and depth-width of joint/crack will cause results to vary. If you have access to either end and are working on expansion joints or nearly straight cracks you might try running a straightened out coat hanger under the rod a couple of feet at a time then pulling up on both ends of the hanger.
 
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