I need to recaulk the concrete slabs around the pool. Not inside, but outside surface perimeter. What to do?

All you need to do is remove the old caulking. Purchase a 1" backer rod material and some self leveling joint sealant. (Thats the grey rubbery stuff currently there) Quickcrete brand comes in bottles I believe and other brands come in oversized caulking tubes. Install the backer rod material into the crack 1/4" from the top of the surface. Once all of the backer rod is in place you can start pouring the sealant into the gap. It can get messy if you try to go too fast. Home Depot and Lowes both have this sort of thing and it is generally inexpensive.The backer rod material serves two functions. First it keeps your sealant from running rampant and secondly allows you to control the depth of your sealant to provide maximum elasticity. Hope this helps.