Shooter 1721 shoots a hw44

I saw a couple of stocks offered for them, one on a German custom stock and grip manufacturer and another I believe on a Czech site..I also think Weihranch makes one for it.

So yes here are some out there for that "pistol".I wonder if the Weilrauch Bullpup stock would also fit it?

The weihrauch bullpup is based on the HW100 so it won't fit. It's as dissimilar to the HW110/HW44 platform in structural design as it gets.
 
Can that be fitted with a stock?

Yes

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https://www.airgunnation.com/topic/hw44-x-tend-stock/?referrer=1