The solution proposed by Given2 aims precisely at avoiding to simply write your IBAN code on your website. By filling up your wedding gift registry the final result will be the same (that is, you will receive the gift amounts directly into your bank account and will be free to spend them as you like and whenever you want), except for the fact that in this way you can also interact with your guests. In fact, they will be able to choose a particular gift that best fits your needs along with the sending of a congratulation message.
We all prefer personalized gifts over impersonal ones as a wire transfer can be.
E.g. in the case of a travel registry, a nice idea could be to choose something like "a romantic dinner", "a massage for two", "an adventurous hike" and so on.
The amounts you are going to receive from your guests will have a very different taste for both you and them, since they will be intended for a specific purpose.
Furthermore, your guests will be free to choose among several methods of payment (e.g. credit card and Paypal), always sending 100% of your gifts without any extra commission fee.
So we are on solid ground when we say that the final answer is no, we are afraid you can't, because of the reasons we have just explained.