I wouldn't crimp new fittings to the thermocouple wire.
Those probes (K type) work by creating a tiny voltage at each point where two different metals meet. If you use different fittings (or even different coated fittings) than the original ones then you screw up the calibration of your gauge.
It is also very difficult to get a good and lasting connection between the fine lead wires and crimp connectors.
There are two methods which are guaranteed to work.
1. Buy mini K type connectors, these are yellow plastic with two metal prongs in them and are made of the right metals to not interfere with the calibration.
2. Strip both wires and crimp them together ensuring contact from wire to wire (i.e. not through the crimp sleeve).
My VDO kit came with ring terminals, the connection started to fail within a year, I crimped them together as a temporary measure but now have mini K type plugs so I can move things around and disconnect easily.
This is a lead with mini K type plugs and sockets. Industrial electricians have them.