Yes that will work very well, no doubt about it at all.

BTW the best way IMO to check the relief is fret high E on 1st stret AND with another hand at 12th fret, pick it in between. There should be enough relief that it _just_ rings freely, i.e. the neck isn't entirely flat straight but there's a very slight bow to it. If it just buzzes, loosen the screw a little and retune/retry, if there's room enough for a playing card to slide under or more, tighten it some.

The nut height is basically correct if it's not hard to fret at the 1st fret AND the first note isn't sharp. If the F is sharp, chances are the nut is a little high, VERY rarely the nut is too far from the 1st fret but I've seen that in a sub-200-dollar ESP-LTD for instance. On Squires it's usually set on the fretboard itself, not after it, and it should be exact always.

In fact I'm a bit surprised you'd have a shimming need even on a cheap Squire, it sort of makes me suspect the guitar has at some point been dropped down hard on its neck so that the impact has forced the neck to lift a little from its actual position. If that is the case, simply removing it and re-installing and tightening those screws well might be enough. Do check for any obvious pull damage to screw holes. If there's some damage, it's best to put some wood glue and matchsticks or toothpicks in the hole and then screw it back on. Wait for a few hours before stringing up if that be the case.

If all that is fine and there's only a millimetre or so of adjust room under the saddle bits then you do need to shim the neck. Those spacers will work fine, sandpaper is perhaps easier to adjust height with and doesn't create an empty space in the pocket, but I'd venture spacers will work just fine. I've seen some amazing things people have done to their guitars...one bass had its neck 'better seated' with cement (concrete!) applied in the pocket and basically glued the neck in with it...go figure what the owner had thought...but even that had worked!

When you're about to do the adjustment, loosen the strings so they're lax but still straight, remove the last two screws entirely and loosen the first ones some, so you can bend the neck a little in the pocket, watch the string heights and try to approximate how much height needs be gained with the shimming. Sometimes it's very little and might be better to just add one flat piece of sandpaper under the neck instead of tilting it at all.

It's really not hard or complicated at all, absolutely a ten-minute job for anyone with at least some common sense - no need to bother a luthier with it.