Your '91 940 SE shift lever appears to be similar to the 740 AW7x shift levers with the overdrive button on the left at the top. The switch itself is similar to the 740 one, but not identical. I much prefer that location compared to the later 940s on the back of the lever. Although I have no experience with yours, it would remove the same way, working around it with a very small slot screwdriver inserted between the side of the switch and the rubber handle to pry and encourage it out. Older rubber may more easily chip and split, so work gently. Working on a warm day with more pliable rubber may help prevent damage. A little bit of WD-40 shot alongside the screwdriver may also help it slide out -clean WD-40 residue off the rubber when done.

Are you sure the switch is gone? Start by double checking the connector under the car to the shift solenoid on the trans. If not soldily clicked closed the connector can open up over time. Also the wire is exposed to the elements and can get damaged.

Another known trouble spot is where the wire comes out at the base of the shift lever where it can chafe through or stress fracture.

Lifting the shift lever up out of the shifter assembly housing for access and repair can be a minor pain, generally requiring disconnecting the linkage under the car and lifting the entire shift lever assembly into the cabin to access the circlip and cap nut so you can drive out and remove the lower shift lever(s). I know some people try to remove the levers from underneath so they don't have to lift the entire housing. Knowing how it all goes together can help. Here's a link to an exploded view of what should be your shifter assembly, including part numbers and availability (Canadian pricing, google can find similar parts listings for the US parts chain)
https://parts.volvocars.ca/a/Volvo_1991_940-SE-23l-Fuel-Injected-Turbo/_51529_5699538/Shift-control--gearshift/GR-61281.html
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now