If you created hyperlinks in InDesign using the Hyperlinks panel, they should appear as entries within the Hyperlinks panel. If you created a link by selecting an object (including a separate text frame), then you will not be able to automatically apply a style to any of the text. If however you create a hyperlink by selecting an area of text using the Type tool, then you can apply a character style to the text in the Edit Hyperlink dialog box during creation.
What version of InDesign are you using? If you have InDesign CC versions, you have the ability to apply a character style to the hyperlink.
Probably in InDesign CS6 or earlier, you would have to apply a character style before creating the hyperlink from text.
I don't think it would matter if you applied the character style before or after creating the hyperlink. Unless I'm missing something.