First, let's understand the method. I pulled in a Togepi at 155 Happiness. The threshold for evolution is 160, so this was guaranteed to be under the cap.
As for how I got it above 180, I used Swift Feathers. According to Bulbapedia...
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Source (With the other things that would break the cap in SwSh if you wanna check those):
https://bulbapedia.bulbagarden.net/wiki/Friendship#Generation_VIII
Vitamins and Feathers do not break the cap in SwSh, otherwise, we'd certainly have heard an uproar about it now that Vitamins are the fastest way to EV train.
The choice of Togepi was also deliberate since Togetic is a happiness evo and I know for a fact you can have Togekiss without Affection boosts in SwSh since I have one.
I promptly chucked 30 Swift Feathers to it and ran to the first trainer I found, which by coincidence, were the Twins in front of Floaroma.
Togepi clearly shifted side to side while Shinx didn't move an inch. That's a clear sign of Affection kicking in.
After that, there was a message during the battle saying "Togepi looks like it wants to be petted..." And that was the kiss of death. Didn't even have time to evolve it. It was clearly between 180-219 Happiness and had affection boosts on it.