WebUI: Convert cr-dialog mixins or parts or remove if unused

Bug: 973674
Change-Id: I0c40034a8d0e33ecec992ead0a9068ac2d81ea1f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1666278
Reviewed-by: Esmael El-Moslimany <aee@chromium.org>
Commit-Queue: John Lee <johntlee@chromium.org>
Cr-Commit-Position: refs/heads/master@{#671102}