What year is your P-Bass Special body?
Unfortunately, there are (or were, more on that below) a lot of subtle differences between Fenders and Squiers. A lot depends on what year each part was made. I know this from several experiences.
1. I tried putting an official Fender Jazz pickguard on a 2008 CII Squier Standard Jazz. I had to do a fair amount of buzzing down around the neck and pickup pocket with a Dremel tool.
2. That same pickguard, before I put it on the Standard Jazz, mounted with little difficulty onto a 2010 MIC Affinity Jazz.
I also have a 2001 CII Squier Standard P-Bass Special with fourteen holes, instead of the usual thirteen. I bought a Mighty Mite Precision pickguard also with fourteen holes. Absolutely did not fit or match up. Not only would I have had to Dremel the hell out of the neck and pickup pockets, but would've had to re-fill and re-drill most of the holes. Suffice it to say, I exchanged that pickguard without altering it.
I've heard from a lot of bassists that until a few years ago Squier's quality control was rather lax. I don't know if that accounts for all the incompatible parts or if it was an intentional strategy by Fender to keep the two lines far removed while still being able to call them "Squier by Fender".
But whatever the reason, their builds seem to be getting close to each other again. There's the example above with the newer Affinity matching up with the new pickguard. Also, I bought a 2009 Squier Active Jazz IV to use the neck with a Mighty Mite P-Bass body (meant for a Fender neck) that is a 95+% perfect fit and a 100% fit for a new Precision pickguard.
All this "proper, or damn close, matching" does seem to coincide with the time Fender started enforcing better quality control within Squier. Perhaps the new doctrine is "people will buy our Fender parts and accessories to put on their Squiers"?
So, going back to your original question; Depending on the year your Squier body was made, a Mighty Mite neck might not line up either. You may have to buy a used Squier (preferably from the same country of manufacture and a similar year), harvest the neck and sell off the body to recoup some bucks.
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