Migrate profile_shortcut_manager_win to use TaskScheduler.

This patch removes all references to BrowserThread::FILE and updates
the tests to handle the fact that the shortcut manager is now truly
multithreaded.

Bug: 689520
Change-Id: I31d145c6ac1685b150a57523d2268796a351f238
Reviewed-on: https://chromium-review.googlesource.com/582367
Reviewed-by: Ryan Hamilton <rch@chromium.org>
Reviewed-by: Scott Violet <sky@chromium.org>
Commit-Queue: Bret Sepulveda <bsep@chromium.org>
Cr-Commit-Position: refs/heads/master@{#491513}
5 files changed