Make sure that you have anonymous checkout enabled. Then open main/register_account.tpl and change the fields you do not want to show from "text" to "hidden"
For example change
Code:
<INPUT type="text" name="uname" size="32" maxlength="32" value="{$userinfo.login}">
to
Code:
<INPUT type="hidden" name="uname" size="32" maxlength="32" value="{$userinfo.login}">
This should work. You might have to do a little formatting to this template to make it look good.