wiring DPST off-on switch for (orig) Dirt Devil vacuum

I had to take apart my old Dirt Devil so as to remove hair wrapped-around just about every moving part.
While doing that, one of the black power-wires (one of the two black-wires that are on the "inside"-side of the switch) pulled out of its wee hole down into the switch.
The wire-end that came out had been "tinned" (solder).
Peering as best I could, with aid of mini-maglight, down into that hole, I saw only that the bottom of the hole seemed to have two (wee) copper strips along opposite sides, and could discern *no* solder anywhere.
So, not knowing what else to do, I tried simply shoving (inserting) the end down into that hole, and, well, it seemed to hold.
(how well and for how long, I don't know)
Anyway, I then closed it up, with the black wire being under no stress either now or in the future, it seemed like...
And the machine works ok -- for now.
The switch is a little rectangular off-on slide-switch.
It had four wires put into it.
(I forget, and I'm not about to reopen it again just to look at the switch, but I think:) that two whites went into the two holes on one end of it, and two blacks into the two holes on the other side.
One black and white being from the power cord, and the other pair going to the motor.
(Anyone recognize this setup -- and switch-type?)
Anyway, here's the question: was just shoving it in the right thing to do?
Should I have got the wire hotter than hell (soldering gun) and melted a bunch of solder onto it and THEN shoved it into the hole?
(remember, no microscope or anything, but with naked eye and flashlight I could detect no solder already down in the hole.)
THANKS!
David
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stranded wire can't be easily inserted into a backstab switch, so they tinned it to make it stiff

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Thank you!
I just learned a new term: backstab.
You said "backstab switch": is that what you meant, or is it the *hole* that's "backstab" (has "backstabbers' in the hole, I suppose)?
David
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Inside are spring loaded clips that keep tension on the conductor, we call them backstabbed
wrote:

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