Although you can use urethane to glue in glass, typically what's used is butyl; a non-hardening rubber. It can be had in either strips or or in a tube. Yes, cutting/cleaning butyl isn't fun, or easy. The "wire trick" described above does work, the tool described above (looks like a hook on a bar with a pivoting handle attached to near center) also works but is a little harder to use. A real glass shop may also have a tool that looks like a 4" grinder but with a vibrating blade on the end instead of a rotating disc. This is the "easiest" tool to use, but none are easy or especially neat. When you've removed most of the butyl & all the glass, you'll still need to clean the surface. Diesel, K-1, & mineral spirits will work.
I'd use 1 or 2 tubes of black butyl (available in any of the big box stores & most hardware stores) to lay down a bead, around 1/4" wide by 1/4" tall, to set the glass in. After cleaning, & before gluing, test fit the glass!!!!!! When you are cleaning, look for "setting blocks" at the bottom edge. Should be small hard rubber blocks that hold the glazing up in the channel. Clean & reuse these blocks! After setting the glass in the butyl bed, tape it in place!!!! Let it cure for at least 24 hours.
I'd advise against using silicone to set glass as the silicone found at retail stores is very poor quality compared to what's used in the glass industry (retail silicone costs $5-$15 tube, industry silicone costs $40-$60+ tube & you'd be amazed how much better the "good" stuff is compared to what 99% of the public uses). Tip: "GOOD" silicone DOES NOT smell like vinegar! "Good" silicone dries soft & looks "dull" compared to cheap silicone.
Yes, I worked in commercial windows & doors for a few years.
