I see what you're saying the tone of site, but I hope the readers are able to distinguish what the site is trying to do and the personality of the solo-entrepreneurs that are featured.
And in the worst case, the picture will be replaced in a little while with another one! :)
I would wait until there were more people on the site, because at this point, if I were to send you a picture of myself in a tie, but then every other picture that showed up on the site was developers making faces - "I" would look like the sore thumb.
This conversation is going to be pointless :) I have a feeling you are going to do really well.
Some people might like a silly photo, other people might be offended by it.
Some potential app users might not care, but some might be more conservative and want to see a more serious image. Certainly a person who may be looking for investment in the future (even somebody who's bootstrapping today) is going to be concerned about the image they project.