I am a big fan of giving the name you want, rather than using the name you really want as a nickname and putting a name you are not so fussed about on the birth certificate.
My DD is Meg. It is not a nickname for her, it is her whole first name (though she does also have a middle name). I love 'Meg' and didn't like any of the names for which it is a nickname. Yes, if I had put 'Megan' or 'Margaret' on the birth certificat she could then choose to be known as Meg, but I didn't like either of these names and I wasnt going to call my DD something that 'wasn't her name' iyswim.
In response to your OP, if you have an Abby (a complete name imo), then having an Izzy really isn't that different. It's lovely, less common than Isabel, Isabella etc.
Naming our child anything could be classed as selfish, as we will never know until it's too late what our children would want to be called, so we call them a name we like.
I know when naming a baby you should think about their name as an adult too, but with all the Isabel,Isabellas around atm, is 'Izzy' really going to be that controversial or bizarre in 30 years time?