You can use a form, something like this, and style the button to look as you wish in your CSS. Use the &loHomeId=`xx` parameter to tell it what page to go to on logging out.
<form id="wlpeUserForm" action="[~[*id*]~]" method="POST">
<fieldset id="wlpeUserButtons">
<button type="submit" id="wlpeLogoutButton" name="service" value="logout">Log Out</button>
</fieldset>
</form>
WebLoginPE does use $_REQUEST, so you could make a link with a query string to tell it what service has been requested:
<a href="xxx?service=logout">Logout</a>
You’ll need to put whatever you decide to use in a chunk, then specify the chunk name in the &successTpl=`chunkName` parameter of the snippet call.
See the "Views" section of the documentation that came with WebLoginPE for more details.