You can prepare your command with parameters and execute using exec sp_execute_remote with the database name.

declare @SqlCommand nvarchar(max) = N'PROC_NAME @PARAMETER = ''' + @VALUES + ''''
exec sp_execute_remote N'InternalConnectionName', @SqlCommand

It's necessary to use the internal connection name because in this case my database is connected with another database.

It is faster than run using another way by my experience.