yes should have said, its always possible of course but would think it unusual for the shock itself to squeak. Suggest a good check over and wiggle of other parts with the shock removed prior to fitting the new ones, although this will not totally recreate the conditions accurately as it will be unloaded.
Re spring compresors. The problem is the spring is longer than its fixed position in the shock, it is "loaded" when fitted and so if you where to simply remove the lower top nut(the one under the nut you see in the engine bay, the shock and spring can be removed as one unit) that holds the spring in place the spring will fly out. So needs to be compressed prior to fitting and removal.
On re fitting a shock its important to re create the camber setting correctly. Assuming yours is correct to start with you can measure the gap between rim and shock body before removal, i used an 11 mill socket as a feeler gauge as its diameter was closest fit, this will help gauge the correct setting when re fitting it is fiddley though.... There is another diy method with a spirit level but ive not used that.