I searched myself crazy to find a solution for this problem. And there is a simple infrastructural solution I want to share with you.
When you publish the non-claims-aware application on WAP you need to enable for that published application on WAP the setting: EnableSignout
Example: The name of your published application is TEST. On the WAP server run the command:
Get-WebApplicationProxyApplication TEST | Format List
There you get some hidden settings that you can't find in the WAP GUI. Default the 'EnableSignOut' setting is "False"
In the result you need to copy the ID of the published application. (Example ID for TEST = b20e2sq4-01ce-e674-5fe7-0709a1e94d63)
Run the command to enable the signout option:
Set-WebApplicationProxyApplication -ID b20e2sq4-01ce-e674-5fe7-0709a1e94d63 -EnableSignout
To cleanup the EdgeAccessCookie (after log on) for the application, use the URL:
https://<FQDN relying Party>/?wa=wsignoutcleanup1.0&wreply=https://<FQDN WAP>/adfs/ls/?wa-wsignout1.0