This doesn’t seem to be very well documented, but there are ways to specify an action for a Skype profile link. This is the syntax
skype:profile_name?action
Examples of such actions are
call
to callchat
to chatvoicemail
to leave a voice mailsendfile
to send a fileadd
to add to contactsuserinfo
to view profile
In this case then, the link to view the profile would look like this
<a href="https://stackoverflow.com/questions/16177332/skype:profile_name?userinfo">Link to my profile</a>
See also the Skype URIs page on MSDN.