You can create a dacpac (containing only the database schema) of the existing database using SqlPackage and then just import it into an Azure SQL logical server that exist on the other tenant.
sqlpackage.exe /Action:Export /ssn:tcp:{SERVERNAME}.database.windows.net,1433 /sdn:{DBNAME} /su:*** /sp:*** /tf:C:\temp\{DBNAME}.bacpac
Here you will find more information about the export action of the SqlPackage tool.