Are you buying new rims, or just new tires?
I have a '99 Cobra Convert, too. She's got 245/45/17's in the front and 275/40/17's in the rear. My rims aren't stock, though, I think they're Cobra R's....? They were on the car when I bought it.
Anyway, I asked one of my tire guys about putting 275's all the way around, and was told that they'd be too wide in the front and might rub. My car is slightly lowered though, so that might be an issue for me...maybe not necessarily for you.
I was also told I'd need different rims if I wanted to change tire sizes. Maybe your guy meant the 275's are too wide for your stock rims, since the stock rims only came with 245's....?
Like 94CobraPace said though, it may depend on which tire you get...some of them tend to stick out. But he's got them on his car, I've got them on mine (well...halfway), and the newer Cobras all came stock with 275's, so you shouldn't have a problem, maybe just need new rims (want mine? I want new ones, lol).