Wiggle Songs in Primary have a specific purpose. The good ones will provide opportunities for stretching and movement in a controlled climate. They encourage singing and following the leader which is engaging the brain. They also will end with getting back into a reverent attitude.
One of my favorites is "My Hands" CSB 273. I actually prefer to lead this one without piano accompaniment. My plan with this is to quickly get the kids attention, allow them opportunities for stretching and movement, but especially to get them to follow the leader. I plan holds and pauses in the singing and movements to see if they can follow me. I will also go faster or slower to check if they are keeping up. It ends with "Clap, clap, clap, then 1, 2, 3. See how quiet they can be" while we fold our arms and sit down. I usually do this song three times through. This takes less than one minute and is amazingly effective.
Sometimes, I throw in a quick stretch, breathing exercise or wiggle song whenever I see the children need it. Just one minute can work wonders.
For example, I have seen well-intentioned Music Leaders give the children rhythm patterns to clap during a song (that has many verses and a chorus) intending to help the children memorize the words. Unfortunately, most of the kids could not do both. So they dropped the singing altogether and focused solely on the movements.
Just because the song has been given movements doesn't qualify it as a Wiggle Song.