This is something unavoidable, even if you click the link manually, the focus will be changed to opened browser. This also applied to all other windows programs.
One way to overcome this, is by waiting for a small amount of time (to give the browser time to load), and then switched back to Excel.
You cannot fast "spacing" and hoping the browser processes in background (like you open the webpage from bookmark), since this is an automated with multi process involved (not single process by browser itself).
Change sub DoHyperlink to this :
Bookmarks