I'm sure most tiles will pop up easy but grinding off the old thin-set residue can be a chore of a job. I would think the choice to do this work will depend on how much noise and dust you can stand and how strong you are. Often saving tile is more work than replacing it. Do the work to reduce land fill waste - be green. Don't do the work to save time and money....

It's really a matter of how well the adhered tiles are stuck. If you can get something like one of those roofing tear up bars underneath and pop the tiles up in full pieces, you aren't likely to generate much asbestos dust. The adhesive can have asbestos also so it could be wet scraped and picked up with a wet vac with a capture bag. If the tiles are adhered such that they break into little pieces, you can likely float where the loose tiles came up and put a new floor over the top. There's also floating vinyl floors that sound like an ideal solution for your situation but I know little about the efficacy or quality of these products.

https://www.houzz.com/discussions/flooret-lvp-in-arbor-brenwick-or-kingswood-or-cortec-harrison-oak-dsvw-vd~5534239?n=631 lot of good info on this discussion.

I preface this reply by saying that it may step on some toes and is not for the easily offended... Think of your floor cleaning like your teeth cleaning: you can brush, floss, and gargle on your own to your heart's delight. But at the end of the day, it can't replicate the cleaning performed by a hygienist in the dentist office. In other words, you need to have a professional cleaning company periodically clean your vinyl floors. I know, most of you DYIers had it installed to get away from carpet, tile, and other flooring that has traditionally required professionals to maintain. Truth is, you DO NOT own the equipment needed to get these floors, particularly the ones with a textured profile, completely clean like they were prior to install. And while the flooring companies didn't outright lie to you (calling it low maintenance rather than no maintenance), they certainly led you astray by letting you to believe that a little hot water or their overpriced, product-specific cleaner was all you needed. So, find a reputable local cleaner to professionally clean your LVP floors. Got kids and dogs? Do you go barefoot or wear outdoor shoes in the house? Get your floors professionally cleaned every single year. The rest of you? Every 2-3 years. In the meantime, stop using steam. Stop using acidic (vinegar) and high ph (ammonia) products. Dump the bleach, Murphy's Oil Soap, Rejuvenate, Bona, Mop n Glow, Orange Glo, and all types of polishes. Only use a neutral cleaner in between professional cleanings. Oh, and those area rugs you put down to cover up the unsightliness of your floors? They're likely voiding your flooring warranty (probably not a big deal because many have already done so with their unapproved cleaning methods and lifestyle).