Sqllogship.exe: replace with powershell?
I coded a script to ship logs manually using PowerShell. You can find it here

Basically it does what native Log Shipping does: it takes transaction log backups, copies to a shared folder and restores to the secondary WITH NORECOVERY.

Some limitations apply: 


Only a single secondary is allowed
No support for STANDBY


I coded it this way because it was enough for what I had to do, which is what you do 99% of the time with log shipping.