S.C.
It depends on the type of gift card. If it's store specific then Kohls.com should still take a Kohls gift card. But, no one else will take it. If it's a VISA gift card, you should be able to put input the number as a credit card number. I know when we use Visa or MC gift cards at the store they're entered as credit cards. I would think it would be the same way.
On another note, I buy stuff online all the time. Most sites have safeguards against getting your ID stolen now, as do most of the credit card companies.
And on a totally different note, I wouldn't buy something from a store if they didn't have an contact information on their website. That seems a little fishy. I'd keep looking until you can find a similar product from a different retailer.