I routinely mix 100mg concentrate, rarely bother with gloves, and have never had any noticeable reaction. The concentrate goes straight from the measuring syringe into the mix bottle or beaker, with the required PG/VG. I don't drink the stuff, or intentionally smear it on my hands. Or inject it in my veins. I always mix near a sink and if I did get any on me I would wash it off immediately. A little reasonableness here, please!
I was a 3 PAD smoker, and I needed 24mg to quit. I am down to 12mg now but I chain vape by intent. If I wanted to vape less I would try upping it. But I enjoy it. I obviously have a high tolerance for nicotine after 40 years of heavy smoking. I never got more than a nice slightly dizzy "high", regardless of how much 24mg I vaped.
We are all different but if a few drops of 100mg on a finger caused anything more than a "nicotine high" and maybe a headache, I think we would read a lot more about it. A few anecdotal poorly reported stories of people going to emergency wards for OD on 100MG... well, it would be good to know how they managed that.
If you think you need gloves, use them. If you think 12mg is "strong" based on your reaction to vaping it, then surely you want to be more carefull because your tolerance is low. If you can't pull nic into a syringe and get it into a container without making a total mess, then surely use gloves. But this stuff is not arsenic. Actually it's just vitamin B3, but that is another story.
Edit: if mixing nic is new to you, then definitely use gloves until you are comfortable handling the stuff.
Pets are another story. When I did this in the same house as my cats, I was VERY careful to clean up and keep them away from the mixing operations. But that is a totally different matter.