To start with, I'd use single quotes in you definition of $mydir so as to avoid escaping your slashes, make it easier to read, and provide a visual cue that no interpolation is going on here.
In Outlook, you can use angle brackets to contain your links, which works with either style of link and avoids the need for %20 spaces:
<file://X:\mydir\my spaced dir\>
Update: Bah! Please ignore my bad advice on quoting, though the Outlook comment still holds. I don't know what I was thinking. Thanks to ikegami and blazar.
<\\myserver\mymappeddir\mydir\my spaced dir\>
I'd like to be able to assign to an luser