Ok, I'll add the TreatChildPageIndexAsSiteMap config setting so you can either set it on the control or set it globally with config.
Css is rendered on the page like this:
<div class="sitemap" id="ctl01_ChildPageMenu_SiteMap1">
I will change it to have this:
<div class="sitemap childpagesitemap" id="ctl01_ChildPageMenu_SiteMap1">
so you can style it with
.childpagesitemap ul {}
etc.
You should not make changes in the code to set css classes.
Best,
Joe