Potentially shocking literally 😉
I’ve had similar in the past, or worse, where old leads have got stiff in use and cracked in the cold, exposing the bare copper.
Just had a look on eBay, as I’m not familiar with that multimeter, but it looks like the probes and plugs might screw together; if so, it should be easy to replace with new flexible wires.
Personally I prefer smooth plastic wires for automotive testing, where there is oil about, as they are easy to degrease.
In the clean electronics workshop I like the more rubbery cables, as they don’t seem to tangle as easily, and also remain more flexible when cold.
As an aside, I’d not used my favourite large screwdriver for a while.
When I took it out of the drawer last week, I noticed the same clear droplets where the plasticiser had suddenly started leaching out of the handle. It has a quite acrid smell, has dissolved the rubber mat lining the drawer, and stripped the paint off the inside where it was close.
p.s. If you ever need a schematic, there appears to be one HERE or HERE
Bill