RE: pickup swaps
IME, strings, and playing style, effect your sound much more than pickups. My basses sound totally different if I slap & pop the poop out of them near the bridge, stroke them gently near the fretboard, strike them with a pick, or pluck over the split coil. Heck, due to a long ago broken finger, plucking with my index finger or middle finger produces two different sounds!
Unless your original pickup is total crap (which is a possibility on cheap Squiers), a pickup swap will not result in a gross change. Pickup swaps generally result in subtle changes in tone/output, your bright and twangy goat will not suddenly turn into a roaring bull. Many, many apocryphal stories of "huge sound changes" involve an unmentioned string swap and setup, as well.