I bought a copy of the Guns Handgun Annual 1985 article on the Sirkis SQP in the hopes of learning more about it. I was not disappointed!
The article confirms that it was indeed a squeeze-cock gun (versus just a front grip safety). OAL was to be seven inches, with a barrel just a tad under four inches (so, more like the Walther PP than the PPK). The action was direct blowback, much like the SD9, but this version had a bolt hold open. Caliber was 9mm with a 9 round capacity. The grips were supposedly rubber instead of plastic.
Perhaps more intriguingly, there were plans for tritium night sights and a 22lr kit. The article also claims that the SQP and SD9 were in production simultaneously. I find this hard to believe, since I think Interarms would have imported some back when they got in the SD9.