Touching with the welding wire is very frowned upon because the wire stickout is never consistent and the wire is never completly straight/bent in the same direction. So your touch offsets are always off by a few 0.1 mm.
Fanuc has a 'wire inching' function that allows you to push/pull the wire for a set duration (set in miliseconds).
If you have to use the wire for touch sensing, be sure that the wire is parallel to the part you are touching to ensure the most accurate reading (if you have a cleaning station with a wire cutter you should also cut the wire to lenght before each touch sensing application - a poor arc off that leaves a big blob of material at the end of the wire will also mess with your offset)
Your search speed also affects the accuracy. The faster the search speed (the speed with which the robot moves towards the part during touch sensing) the lower the accuracy. Default on Fanuc is 10mm/s IIRC, maybe lower it to 5mm/s? This is a much bigger issue with wire touching than it is with the gas nozzle.
Most use the gas nozzle instead of the wire which is much more accurate and consistent, but the welding torch must support gas nozzle touch sensing and you have to set it up on the machine.
TLDR.: Dont use the wire for touch sensing. Use the gas nozzle (if supported)
Your explanation was a good and point me on right direction. A couple days later of my initial post i was back to robot and manage to dig thru system and found the 'wire inching' function. After few tests i have found the right amount of inching time needed for the different type of welds i have. I know is not accurate as having a wire cutter station, but it + seam sensing are working good enough for what we need here.
Big thanks to you @ NoBugsOnlyFeatures