This test probe is based on an SMA connector and spare test probe parts:

Side view:

Parts used:
Pomona test tips: Kit model 6354 (Five different sizes, pack of 10 total)
SMA socket: Tyco 3-1478955-0
PTFE tape (plumbing tape)
Epoxy adhesive (Araldite)
The SMA socket insert has a diameter of 1.25mm

The Pomona test tips are 1.02mm (0.04″), so they will easily fit.
The spring tips are 0.75mm in thickness at the tip end.

There are two long and two short non-spring-loaded test tips in the kit, so up to 4 probes can be made. The remainder six tips are all spring-loaded, so possibly not ideal. However, it is possible to convert them, by soldering them as shown here. This is easy to do if you put a tiny piece of insulation tape over the area that you don’t want the solder to cover. The tip was clamped to a small pair of pliers with an elastic band, to hold it in place while soldering. Afterwards, it can be gently filed if the solder is not uniform (in my case, I did not need to file it, because the solder bump was under 1.25mm in diameter, so it fitted neatly in the socket.

Probe parts:

One of the probes was inserted inside as a quick test:

The crimp end of the SMA connector was cut off with a junior hacksaw. This is not essential, but I wanted to reduce the capacitance.The end is then filed or sanded to keep it clean.

This is the probe with solder to make it non-springy:

The probe needs to be insulated to prevent it from touching the shell of the SMA connector. There is no room for heat-shrink tubing, so instead PTFE tape was used. The tape was wrapped around most of the probe from the solder point, and then inserted into the SMA connector:

The excess PTFE is cut off with a very sharp scalpel (otherwise it just stretches!), and then  a blob of Araldite was applied. It is hoped that the sanded end of the SMA connector provides a good surface for adhesion. For future probes, I may apply some araldite to the PTFE portion of the center probe before inserting it into the SMA shell.