Going by what I've read, so I might be wrong: -
It is illegal to obtain and use a DNA sample without consent. So there are two types of test available:
ILLEGAL: get a "home testing kit", take samples from the husband without his consent, take samples from the kid, and send them off to be analysed. Problem: this is only possible after the kid has been born, you can't get at the kid's DNA until then.
LEGAL: a clicic sticks a needle in, gets a DNA samole from the fetus, and compares it with a DNA from a consenting possible father. Problem: that would involve telling the husband. If the test is with the punter instead (and what about other punters?), he might have to disclose his identity, and runs a small risk of being clobbered for child support if he IS the father, and if he can be traced. There is also the very considerable expense.
SEMI-LEGAL: clinic compares kid's DNA with an illegaly-obtained sample from the husband (or an anonymous sample from the punter, no proof that he consented). I do not know if the clinic would be breaking any laws here, as they were not responsible for obtaining the DNA. I suppose she could ask them.
My advice would still be SEVER ALL CONTACT. This mess is NOT the punter's responsibility. And expecting him to pay is VERY dodgy, no way should that have even been suggested, and that makes this a likely scam. If genuine, it's still very likely that hubby is the father, and the WG needs to chill out! And even if the punter lied about the condom and actually barebacked her - which would explain why the WG suspects him - he still needs to SEVER ALL CONTACT and run away!!!
The fact that he didn't use an anonymous punting phone could be a problem, but if he can't find the number in a Google search, nobody else can - except the police. Unlikely that the Child Support Agency would get the police involved without some sort of evidence that he is the father, or that hubby is not.