A simple Case for the NVIDIA Shield Remote. There are two versions, with access to the Netflix button and without:

• “With Netflix” to have the button NOT blocked
• “No Netflix” to have it blocked

The back is flat so the remote can actually lay on it. You can finally press the buttons without picking it up! And while the case makes the remote bulky, it feels better and more ergonomic in your hand (at least for me).

You can slide in the remote from the top and use the retainer to keep it inside (but the clearance might be small enough to make this obsolete). No tool or glue required.

Note that the retainer is not symmetrical: the rounded corners in the gap should point away from the remote.

If you prefer a fuzzy skin, you can use the included modifier. Just make sure the relative position is 0 on all axis and that only contour is selected. The first and last two layers (or 0,4mm) are not included in the modifier. I chose 0.3mm for both point distance and thickness, but you can choose whatever you prefer. 

Use automatic tree support. You can put a support-blocker for the small hole on the very top, or not bother at all because it makes little to no difference. It could work without supports, but I have not tested it.