Hot Shoe and small size do not go together.
Good zoom and small size are hard to find.
I only came up with one camera that fits your description, but it is a good one.
Here is a link to specifications:
Does anyone have recommendations for a camera that has a hot shoe for the flash, a good zoom (over 4x) and does movies as well? Ideally I'd like one that's smaller in size, but the features are the most important thing. I also want one that does good with the autofocus. Thanks for the advice in advance!
By the way - I currently have a Canon Powershot s50 that I like a lot, but lacks in the zoom and flash.