Can i alter a database to single user which is configured in log shipping
There's several parts to this question:

Do I need to set the database to single user mode to change the compatibility level? No.

Will changing the compat mode from 90 to 110 break log shipping? No.

Can I change a log shipped database to single user mode? Yes, but don't do that unless you have to. Sometimes, you might not end up being the single user (like if someone else grabs the connection from you, like if your SSMS crashes after you set it to single user mode.)