Yes, cut the wires and crimp on spade connectors for future ease of replacement (I am also fairly sure 0.187” is what you want - DumbAss is, in fact, NOT a dumbass).

Follow LTG’s advice for learning to solder. I’d further recommend that you invest in a decent quality temp-controlled soldering station (if you can swing $100, the Hakko FX-888 is highly recommended and might be all you ever need) and a selection of 3-4 tip sizes (0.8mm, 1.2mm, 2.4mm, and 3.2mm chisel tips are sufficient for most any pinball repairs other than SMT reworking). Start with a temp setting of 325C (resist the temptation to set the temp too low because it will take longer to make the connection and is actually a higher risk to damage the component being soldered than a higher temp for shorter duration).

Get some QUALITY 0.032” 63/37 Sn/Pb rosin-core solder (Kester “44” is about all I ever use). Rosin is derived from pine sap and contains abiatic acid which undergoes a heat-catalyzed reducing reaction with surface oxides, cleaning them from the metal and allowing the solder to wet/alloy with the parts being joined. I recommend against water-soluble fluxes because they MUST be thoroughly cleaned from the joints after soldering. I also advise against learning with Pb-free alloys as they require a higher temp and are more difficult to work with and achieve a solid connection. 63/37 is a little easier and quicker to flow than 60/40 because it is a eutectic alloy (has a specific melting point rather than melting range); the only disadvantage is that the connections are slightly less physically robust than with 60/40, but I’ve never encountered this as a problem in my games/other stuff.

Watch a video or two, then go to town practicing on junk circuit boards, wire scraps, etc. When you get a little confidence, assemble a reasonably simple kit or two, and if you are successful you can then feel confident about working on your games. (I recommend Elenco and Velleman kits, as they have excellent build instructions and PCB quality and a wide selection of kits); a couple of specific selections which will be useful finished products:

Bench Power Supply (https://www.electronickits.com/bench-acdc-power-supply-kit) - will give good experience with both point-to-point and PCB soldering, as well as skills like heatsink prep and assembly, and works well as a bench PS.

Digital Multimeter (https://www.electronickits.com/digital-multimeter-kit-training-course) - great educational build manual, and everyone needs a decent meter with the functions this one has.