I would really recommend that you replace the headliner. Couple of reasons. One, you can retain more heat with the insulation. Two, it does offer a bit of sound deadening, more or less depending if you do replace the fiberglass we all hate so much. Three, as you noticed, the cheap lights that Clyde Cessna chose to put in leak light everywhere otherwise. And the fourth and final reason. The e'ffing FAA wankers that know nothing, but you just gave one of these wanks a reason to turn your crank. Open the door and eventually some kind of weasel will slip in to give you some fun. That is unless you have some very convincing paperwork to back up the omission.
I have a love hate thing with skylights. My first 185 didn't have them. It had everything else, but no skylights. Shortly after I got the 185, Dogpilot got his first namesake Birddog. Ahhhh, skylights, lots of skylights. Lots of skylights that leaked water all over the middle of the seat every time it rained no matter how many time I sealed the silly things. Then later, as Dogpilot moved upward on the evolutionary path, his hair started to thin, to the point one might be tempted to say, bald. Now, I have to wear a hat under my headset or my sensitive bald head burns. Then there is the occasional placement of the errant star that seems to like to put excess sunlight on stuff I am trying to read in the cockpit. But...there is the one time the skylight may have saved my life. My little inner voice, when not detailing my numerous failing, managed to stop berating me for a moment and told me to look up. There was some kind of Piper, I think a Lancer, decending directly on top of me over the Lakeland VOR. So aside from that, after having them in several aircraft, they do allow you to look at the underside of bridges as you fly under them but not much else. I no longer covet them.
So if you decide to replace your headliner, I used to get mine from ACME headliners, yes ACME. You would send your old one in and they would make a copy with lots of extra material. This along with a burn cert for the material. Unfortunately they will not make aircraft ones any longer. I assume they got sued after one of their headliners was involved in a major headliner related accident. I now get them from Airtex. Who on my last skylight equipped 185, made up a second special one, since the first one seemed to not have enough material to complete the job after tucking it around the skylights. They did it really fast and free.
The last reason I might put out for keeping the headliner. Bumping your head. Most C180/185's had a piece of foam rubber on the cross member running across the cockpit under the headliner. This lessened the impact on my poor, much beat up head. Now if you exposed all the other sharp bits of metal in the overhead, I would be compelled to get my head all beat up on all of them at one time or another. Aside from that, it does look a bit like a rusty '82 primer covered Chevy Camaro when you leave the interior out. To me that is. You may find it a minimalist, hipster thing of beauty. Taste varies.