To download a file from a public bucket using wget, just use the syntax:
wget http://s3.wasabisys.com//You'll want to be sure to use the specific endpoint for your bucket depending on the region. See What are the service URLs for Wasabi's different regions? for details.
An example of wget would be:
$ wget http://s3.wasabisys.com/wasabisupport-test-public-east/hawaii.jpeg
--2019-06-29 13:10:04-- http://s3.wasabisys.com/wasabisupport-test-public-east/hawaii.jpeg
Resolving s3.wasabisys.com (s3.wasabisys.com)... 38.27.106.21, 38.27.106.14, 38.27.106.16, ...
Connecting to s3.wasabisys.com (s3.wasabisys.com)|38.27.106.21|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 838602 (819K) [image/jpeg]
Saving to: ‘hawaii.jpeg.1’
100%[===============================================================================================>] 838,602 --.-K/s in 0.02s
2019-06-29 13:10:04 (43.1 MB/s) - ‘hawaii.jpeg.1’ saved [838602/838602]-mike