Need a small compression rod for stabilizing my dryer
I would suggest that you get yourself some high density foam material similar to the type used for padding furniture cushions. You can get this material in various thicknesses so you would want to measure the gap from the sides of the dryer and the walls and purchase accordingly. One Example

The idea is to cut the high density padding into a square of say 1.5 or 2.0 feet on a side. Then squeeze that in between the wall and the dryer sides. You will want the material to be under some compression when it is installed. It may be necessary to insert two pads of different thicknesses on top of each other to get the needed space filled up with some compression. 

This approach has some decided advantages as follows:


The foam material will act to muffle the sound coupled to the wall. Your idea with point contact will more likely couple sound right into the wall.
The foam pad extends out over a larger area of the dryer sides to provide stability and to reduce the drum head effect that metal appliance walls can create.
The pad spreads the compression load over a large surface of the wall to prevent wall damage. A point type of compression assembly would have to be positioned over a stud to ensure that it does not eventually break into the wall. This would be particularly an issue for the very common drywall material made of paper and plaster material. With the foam that load gets spread across a large area.