That type of Curt adapter is what you're looking for. That particular kit has black extra wire to go up to the battery and a longer green wire to go over to the right turn signal, neither of which you will need. You can get similar converters from Hopkins and others. That particular Curt kit isn't too badly priced, but check out Amazon and even better check out your local UHaul centre and local RV dealers who commonly have such converter kits available.

Princess Auto (kind of like Harbor Freight to you US types reading here) seems to only be carrying non-powered converters at the moment. I've been thinking that if the UHaul trailer is all LED lighting and being that all the wires in that connector come direct from the front of the car ahead of the bulb sensor, that you may be able to get away with a non-powered converter and with minimal affect on bulb brightness and the flasher interval. It would save you a wad of money, for example Princess Auto has one in stock near you for $15. At that price it may be worth the experiment. If you then drive to your local UHaul centre you could ask to do a test connection on that or a similar trailer to see the effect on brightness and expecially the flasher. If you convert you're 940 park/brake lights to LEDs (as I've recently done using Auxito white 1156 & red 1157 bulbs from China, post back if you want the particular ones I chose and also recommended by Bill here) a non-powered converter should work fine. Trickiest bit is the turn signals. The flasher needs a load on it and you need to find special LEDs or else switch to a solid state flasher. That's an experiment I'll attempt some other day after I've had a chance to investigate the options.

As for using crimp taps, electrically they are perfectly adequate for the kind of currents we're talking here. Pro's use them. Yes, it won't look like a factory hookup. If you're a purist for electrical connections then just cut the needed wires leaving 1"-2" of tail and solder your wires in a "Y" using heat shrink. Double check the length of the 4-pole wire. For the kind of use you have, I wouldn't bother with an external trailer connector. I run mine it into the wagon hatch and leave it loose. I double wrap the final 4 feet in black electrical tape (triple wrap it against bending at the connector and where it will go out under the tailgate close to the latch being careful to avoid the latch itself). Plastic wire harness cover is a bit thick for the job going out under the tailgate.

Now finding a 10-pole mating connector to make a plugin harness is going to be a challenge, also not going to be overly cheap. I'm not sure if it's perhaps Molex. You can try finding it on Mouser. Have a look at Dave Barton's site https://www.prancingmoose.com/blackvinyl.html. There's 3 pages of assorted stuff there. He's spent forever trying to source assorted connectors for our RWD Volvos. If you read his notes you'll get clues of the connector brands Volvo used back in those days.

Now here's something amazing I just turned up. Volvo did have that trailer harness available. I can't find the 700/900 part no, but I think this 2001-on FWD harness may be compatible (I'd say a 75% chance) and it appears to still be available in the Volvo parts chain https://www.fcpeuro.com/products/volvo-tow-hitch-wiring-harness-genuine-volvo-30681980#description. Note that it seems to include the converter. [Edit: nope, it's a rubber gasket for going through the body, so you'll still need to splice in a converter.] It has a standard North American 7-pole trailer connector. You can buy 7-pole to 4-pole adapters at places like Princess Auto, again I see local stock near you. [Edit: I just found the original 1994-on 900/V90 Volvo trailer harness on Skandix, Volvo p/n 9134962 https://www.skandix.de/a/1016645/, no converter and NLA in the Volvo Euro parts chain. I note that the connector is separate, maybe so you can splice in a converter. I've double checked the wiring diagram and you definitely need a converter for either 4-pole or 7-pole trailer wiring. I still think there's a chance that FWD one for the NA market might work if the connector is the same 10-pin and you were willing to hack it off and splice in a converter, maybe needing to move a couple of pins around.]

As for what that other grey plug is, it's obviously factory. Without checking the manuals, I'm fairly sure it was for the optional remote CD changer used with the CR-915 stereo. In sedans it lived under the parcel shelf, in wagons it lived under the hatch. Check your manual. It's component 6/15 in the '95 manual. The North American cars didn't get that harness either, so likely factory installed in Europe the same time that trailer harness was installed. I'm not sure why Euro 940s may have that trailer harness as standard, while not in the North American cars from Halifax. Maybe has something to do with North Americans using mostly pickups for towing.

(I see your profile here says you're in NB. I'm on the far left coast in BC.)
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now