Print "hairs" without support in GrabCAD Print
There's no way to do this in GrabCAD Print alone, but you can achieve it using Insight, which you can reach from the Apps menu in Print. The steps are as follows:


Open your STL file in Insight.
Go to Modelers → Setup… and set the printer, layer height, and material to the same as in Print. If you get these wrong, you won't find out until you get to the end and Print refuses to print the part.
Use one of the red icons to slice your print, with or without the wall thickness filter.
Use the red and green icon to generate support. You'll notice all of your hairs are now supported.
Go to View → Display options…. Set View only to Group curves, and then Group to view to All support. This filters out the (red) model curves, showing only the (green) support curves.
Go to Edit → Delete…. Then left-click and drag a box around the unnecessary supports. For my part, dragging the 3D view to be top-down made it easy to drag a box around just the hair supports while leaving the other supports untouched, but it'll depend on the shape of your part.
In the right panel, make sure the delete mode is set to Curves, and click OK. Now all your supports should be gone. At this stage you can set the display options back how they were if you want to inspect your model further.
Use the green circle icon to create toolpaths
File → Save As… → Toolpath to save as a .cmb or .cmb.gz file.
Go back to GrabCAD Print. (You can close Insight now if you want.)
File → Import CMB and choose the file you just saved.


CMB files show up very boxy on the tray view (and Print will display a warning about that), but if you go into slice preview mode, you should see it as it was in Insight, with just the right supports.

There's one caveat with this method. The slicer generates the base as a single contour, so deleting the supports under the hairs doesn't remove that section of base, and AFAIK you can't make the slicer recompute just the base (so generating support again would put the original supports back). You could edit the base contour before step 8, or disable the base completely in the support options before step 4, but the amount of support material saved probably isn't worth the effort.