FYI for the benefit of others: 7/0.2mm is 0.22mm2 or 24AWG.
I “love” how OP’s question is essentially “what’s between Kynar and 24AWG”, as if an insulation material were on the same axis as wire size…
OP: what is it you want? Thin or thick insulation? Something flexible? Something rigid? Why not use softer stranded wire (i.e. something with finer stranding and softer insulation)? You can get ~24AWG wire with 128 strands, which is far, far limper than 7/0.2mm. Silicone or soft PVC. PVC is super easy to strip, so you can use a full automatic stripper. (Some, but not all, silicone works in those.)
If you want something stiffer with thin insulation, try mPPE insulated wire, like UL style 11027 (many vendors) or Alpha Wire Ecowire or Ecowire Plus.
Or if possible, how about not soldering wires at all, and instead using better probe holders that can just hold the probe tip in place?