I've been using Breakfree CLP for about 3 1/2 -4 years ever since Birchwood - Casey discontinued my favorite gun product which was Rig #2 Oil. The Breakfree CLP I have has not changed (since I have started using it) and the newest batch I have is approximately a year or so old. When I bought it, I bought 3 bottles and so if they have changed the formula recently I am unaware. Seems to work just fine and does not smell any different. In fact, I have a metal box left over from dark Chocolate that I use to store an oil rag treated with CLP. I use it in my work shop after using tools to prevent rust. I usually use the oil rag at least a half dozen times a day and have not noticed any issues with my skin. When I use it to clean and lube firearms I do wear Nitrile gloves - but that is not just to keep the oil off my hands, it's mostly to keep the lead and primer residue off my skin.
Lucas Extreme Gun Oil is a relatively new product and I do have a couple of friends who love the stuff. Personally I have not tried it yet but from what I've read, it is still a Petroleum based product. You might have developed an allergy to what ever ingredients are in the CLP but again, if they have changed the formula I am not aware of it. Skin allergy's do exist.
Since Lucas is a product that I've not tried yet, I can't tell you wether or not it is safe for clear coated firearms. I'd strongly suggest calling Lucas and asking them - they should know. You could also call S&W and ask them as well.
In general, it is a good idea to wear gloves when working with any petroleum based products regardless of manufacturer. Your skin is not chemical proof ( it is permeable ) and pretty much anything we use does work its way into our bodies.
About the safest products one could probably use is plain old Mineral Oil. From what I understand, Hoppes, Starrett, etc. is nothing more than Mineral Oil and should be relatively safe for your hands. Because of that it probably isn't as effective for cleaning lead and carbon deposits off guns, probably isn't as good at preventing rust, but for sensitive skin would probably make more sense.
We all like to think we have a miracle, do-all product to use on our guns, but the truth of the matter is that unless your firearms are in extreme environments often, neglected or abused, almost any mineral based gun oil will be fine. Unless you live in a super rainy and wet environment, extreme cold or damp, Hoppes Gun Oil (mineral oil) should be just fine. I know some who just use generic Mineral Oil from the Drug or Big Box store and it works just fine for them.
Bottom line is if you do like the Lucas - call the Company and ask them your questions regarding how safe it is for finishes. I'd also ask how safe it is for your skin and liver.
SAFETY DATA SHEET FOR LUCAS:
https://lucasoil.com/pdf/SDS_Extreme-Gun-Oil.pdf