The one-touch style clamp is interesting and looks like you just bend thick end over and clamp it. If the boots come with other types of clamps (more commonly called Oetiker brand's ear-type and non-ear type), then parts store will have free loaner tools. Same for the common aftermarket double-band type clamps.
Just make sure before banding up the inner joint, make sure the length of the axles are as specified. Burp the boots if necessary so you'll have the least stress on the boots while in operation (that the boots are not been unncessarily extended or compressed).
And torque the axle nut with the wheel off the ground to spec. Get a helper on the brakes to hold the axle. To make sure the wheel bearing will have its longest life.
I also add a little more grease (say 0.5 oz) than the upper spec limit. But that's just me. And you might want to change out the inner axle seals while at it.
If the boots are intact, then I personally would not remove the outer joint to clean it. I would just wipe off the grease off the outer (after moving the inner joint so you can slide the outer boot over) and pack in the new grease. If you don't plan to disassemble it then don't just spray brake cleaner into the outer joint as it won't flush out completely and will eventually ruin the grease, joint and boot.
Here's a member's inner boot replacement thread on the Corolla. But there are some discussions on tools and he's got some pictures on holding the hub and such that may be useful.
Replacing inner CV boot instead of whole axle?