IIRC you are meant to clean the chain completely (i.e remove all other lube inside and out) before using squirt. Quite what will happen if you don't do this is anyone's guess …
I used Squirt (for a few months*), once applying it to a new KMC X8.93 on top of whatever factory lubricant that chain comes with. The result was an unbelievable gunge that felt draggy even when pedalling down the road (not just when turning the cranks backward by hand).
So how stiff are these stiff links, Pedal Castro? Just highly viscous or mechanically binding? If the former, it’s probably just Squirt reacting with existing lubricant, which, as Brucey says, should be thoroughly removed first.
* As Biggsy found with other dry lubricants, Squirt is not as clean as claimed. Furthermore, although it tests very well in the laboratory for low friction, I found it to be draggier than cheap oil after a few hundred kilometres of typical dirt. Since I’m not willing to deep-clean my chain every 300 km (about once a week for me), that put an end to my experimentation with Squirt. Besides, it’s simply too expensive for my taste, not least because it has to be so frequently reapplied whether or not you deep-clean the chain before doing so. But don’t let all this put you off. Just make sure you apply it to a degreased chain.