By "hidden", do you mean "removed" under display options?
As a workaround, you can also set (in display options) to have tangent edges use a different font.
So, while dimensioning, the tangent lines are visible, but distinguished from the standard edges for ease in selection.
Then changed to removed when dimensioning is completed.
Not a great solution, but perhaps a viable one for your situatiuon.
EDIT: Another thought is to change the tangent edge font to a centerline and then apply the edge filter.
There's centerline filter so the thinking is that by switching tangents to centerlines, they'll be excluded from selection.
(You also filter for centerlines and then invert the filter to exclude only centerlines.)
I'm not too confident on this one, but I figure I'd toss it out there anyway.
I'm not at SW at the moment, so I can't test this edit.
Welcome to the club.....zoom in and dial up your hand-eye-coordination is the only option.
To note...you are more likely to grab the 25 11/16 then the other one.....
I wished SW would do something about the 1980 selection speed in drawings
Hopefully this will help.
Options > system options > Drawings > Uncheck "Select Hidden Entities"
You will still have to select the edges on a tube with tangent lines but at least you won't select the tangent lines if they are hidden.
You can temporarily toggle that same setting by holding down the alt key....but the basic problem still exists.