I found solution which works in our environment.
It is not possible to transfer credentials through double hop without Cred-SSP, but you can run something on target machine without first hop.
The simplest way is to use psexec with -s flag (run remote process in the System account), final string was something like this:
psexec \\someHost -s robocopy "\\stagingHost\Staging" "\\someHost\C$\Staging" /MIR
Also you can start some PS script in same way, just ensure that script execution is allowed on remote machine:
psexec \\someHost -s "\\stagingHost\Staging\Script.ps1" SomeArg1 SomeArg2
Check this article, to understand how psexec works. While service on someHost