Cornwall in February will be damp, miserable and quiet. I know, I live there. It's certainly not somewhere I'd consider as a stag do destination, unless they've got specific reasons for it.
Accommodation will be cheap though. And if a large group are staying in self catering, his share of the cost might be quite small. But going out could be far more expensive than the accommodation. So it really depends what they've got planned - if it's mostly coastal walks/hiking and beers from the supermarket then it may be cheap. If they spend the whole time on pubs crawls and dining out, that'll get expensive.
Ask him what his budget is for it, what they've got planned. Not all stag do's are debauched alcoholic mayhem, it depends on the blokes involved. You'll probably know if him and his mates are the sort for 'sensible' weekend away, with a round of golf and some sightseeing, or whether it'll be liver pounding, wall to wall boozing.
Bear in mind that the budget won't be determined by him, he'll have relatively little say in what he ends up shelling out for. So if he gives you a figure that sounds too cheap, double it! And as he sounds like he's not great with money, restrict his access to cash, and credit cards if he goes.
Similarly, a family holiday can be as cheap or expensive as you make it. So no excuse for never doing something, even if it's going camping somewhere not far from home.
Gambling away £40 a week (that you know of) is not appropriate for someone with a young family who's pleading poverty.