Based on my understanding, there is no direct way to filter the files via copy activity.
You can follow the below process:
a) Use get meta data activity to get list of all files from your source location
use another get meta data activity to get list of files from your source location with file name beginning with ~
b)Then use filter activity to get the other files
the below link can be used to get the filter data :
c) then use foreach iteration to copy it