Those appear to be light tunnels, rather than sky lights. Personally, I would leave them, if they are in good condition.

Flush glass would help. Technically these aren’t skylights (skylights are glass that you can see the sky through) but rather solatubes- great product but especially the curved one looks like a 90’s builder light fixture.

Solar tubes....you get free sunlight.

Your particular skylight looks a bit old fashioned (is it a tube?) but skylights themselves can be quite modern. We have one in our kitchen similar to this.

Mid-Century Modern · More Info

If it's a tube/tunnel, how about something along these lines:

VELUX Sun Tunnels · More Info

I wouldn't give up the extra light.