I came across a problem recently with SharePoint 2013's new Access Request mechanism. It's a great feature, the only problem is, it requests Site Collection admin by default apparently to approve the users that request Access. I have found a work around for this, that will allow site admin's of sub sites to be able to approve/reject access requests for the sub site they are set to receive them for.
There is a list that gets created when an access request happens on a site called "Access Requests", this list doesn't exist till a request happens. Once this happens, you open SharePoint Designer 2013 and navigate to the site.
Once on the site, navigate to the All files menu on the left hand side, then "RIGHT CLICK" the Access requests list which should be in your list and select 'properties'.
Now on the Properties screen, in the Customization Section is a Permissions for this List link. Click this, then you can now set permissions to the users your want to be able to approve Access requests for that site.
This list is generated for each site, so setting this permission only affects that site.
Let me know if you guys found another solution to this or have any questions. Thanks!