Seeing more and more of these caps on these boards failing.... If it were mine and you have the skills to do it successfully - I would replace all the caps. Earliest WPC is 30 years old now...

Yup, those caps are failing. I would get rid of them sooner rather than later in case they breach/leak.

Your souffle is almost ready!

Chris Hibler has a good video on you tube on how to remove these snap in caps...using a wide soldering tip that hits both prongs of the cap...I dont have one of those ,but I use my desoldering gun along with a regular iron and (with help) hit both prongs at the same time...also remove and resolder the old solder before all this...

Go standard, radial caps when you can find them. Regular radial caps have less chance of ruining the plating within the holes when changing them. Nichicon is one source for caps that will fit. UVR1E153MRD for the 15000uF, 25V caps, UVR1V103MRD for 10000uF, 35V caps.

The snap cap does not give better protection against vibration, they are used to hold the cap in place during the wave soldering process.

Is there a way of testing CAPS on board with DMM or do you rely on the cap swelling on top

I'd be changing way more than that. All the Electro Caps will be stuffed or close to it.
Including the Smaller ones on the 5 & 12 volts rails

Yes and if it were mine, I'd be sure to double check C2 at a minimum:

https://pinside.com/pinball/forum/topic/psa-wpc-driver-board-c2-leak

A DMM cannot test capacitors (well, not as a standard feature anyway).

You need a special meter called an 'ESR' meter for Effective Series Resistance. This can test most caps in circuit and usually will give a pretty accurate idea of the condition.

In the end though, these boards are 30++ years old and that is far in excess of the caps stated shelf life WITHOUT being used!!!

If you're interested in getting one, this is the one I use:

ebay.com link: Peak Atlas ESR70 ESR Meter

Although, I rarely actually need to use it. Most of the time when I pull I cap, I'm replacing it anyway.