Two thoughts, if you don't really want to wear skating clothes just yet and don't want to wear street clothes, just buy some leggings for skating in and a top. These can be your skating clothes for the time being (most of my tops are just regular tops that I wear for skating and so I think of them as skating tops).
Alternativel, as a coach once said to me, if you're wearing nice skating clothes it puts you in the right frame of mind for skating and can actually aid the learning process. It makes you think you're about to undertake an athletic activity. You wouldn't go down the gym wearing jeans so why should skating be any different?
And if you do start wearing a skating skirt and tights at this stage, you won't have a mental problem putting them on later. I used to be very self conscious skating in a skirt. I then made a mental decision that I was going to do it, and made sure every time I stepped on the ice after that I was wearing a skirt. I'm now not self conscious and switch back and forth between skirts and leggings without issue and wear what suits my mood (although always a skirt for dance).