Yes! Add an expression control to the layer you want to wiggle.
Effect -> Expression Controls -> Slider Control
In your wiggle expression, highlight one of your parameters and pick-whip the slider control. Now your wiggle parameter is linked to whatever the slider control shows.
The slider control is keyframeable, so you can start your wiggle amount at 20, and have it gradually become zero at a later point in your timeline.
Here are some COW tutorials related to this topic:
Expression Controls Parts 1, 2, and 3
https://cowcast.creativecow.net/podcast/after-effects-expression-controls-part–32
https://cowcast.creativecow.net/podcast/after-effects-expression-controls-part–31
https://cowcast.creativecow.net/podcast/after-effects-expression-controls-part–30
Here is another one from Andrew Kramer:
Basic Training 9 – Expressions
https://www.videocopilot.net/basic/ae_expressions.html
Good luck!
Nate