This really is NOT rocket science. The headset has pretty standard tinsel cable which is a real pain to solder. The first thing to do is identify the two pairs in the 4 core cable. find an AA battery - grab one of the tinsel ends, scratch the enamel coating of with a sharp blade (it’s not really enamel any more - usually a polymer coating now, but it has to go!). Put one of the tinsel ends on the bottom of the battery, and one of the others on the top, with the headphones in your ears. One of the three will crackle - these two make a pair. the other two will be the other ear pair. Make a not of the colours.
Next - remove the cover from the 2.5mm jack plug - it’s a 3 circuit type. The sleeve is the common and one off the two others will be for the speaker, and the other for a microphone - which you don’t have. The radio detects the microphone impedance when it is connected and switches to transmit. The other circuit is the speaker. So take your pair of colours that crackled on the battery, and try sleeve to tip and see if you hear received audio. If not, then the connection will be sleeve and ring, no connection to tip.
Next issue will be soldering. Once you have scratched off the insulation just at the end, you need a VERY hot iron - 25W should do it. Apply the heat, press hard and apply solder, which should flow to where the insulation was removed. Do the same to the other three conductors. Next is to tin the plug terminals. If the plug has a hole on each tab, enlarge it so both tinned ends of each pair go through the hole, and then with a pair of pliers squash the hols to mechanically grab the tinned ends. Then you can apply the soldering iron and add some solder, before the **** plug melts. If you don’t fancy that - then with a meter, find the correct connection on the moulded end you have, and make the joints externally - A good trick is to slid onto the cable before you solder it, some sleeving. A tube - maybe even a sliced off bit of biro tube. once you’ve soldered, insulate with a thin bit off tape and test. If they work and the joint is good, then slide the tube over the joint, squeeze in some epoxy from both ends and then shove in the cable a bit further and leave the epoxy to set.
The only concern is that on some radios, the combined mic/spkr plug prevents the internal microphone being selected. Inserting the plug makes the radio believe the external one is to be used.
This isn’t a hard electronic job, but is very dependent on how well you can solder.
I would avoid even thinking about adaptors, because what you want isn’t really possible with standard adaptors - and 2.5mm adaptors are awful unreliable things that strain the 2.5mm socket badly.