Nested Dynamic Query with SP_EXECUTE_REMOTE for binding the Parameters
SP_EXECUTE_REMOTE in Azure works very similar to native sp_executesql. So you should be able to bind the params &amp; values. But I believe there is a limitation that you can't get a output param value from it. Try this and see if it works for your case. Thanks.

EXEC SP_EXECUTE_REMOTE
    N'External_DB1',
    N' DECLARE @param1 nvarchar(max)= @param1_from_sp_DB2, @outparam nvarchar(max)
    EXEC SP_EXECUTESQL N''EXEC DBO.[sp_DB1]@param1,@outparam OUTPUT'',
    N''@param1 nvarchar(max),@outparam nvarchar(max) OUTPUT'',
    @param1 ,@outparam OUTPUT
    SELECT @param1 AS Paramvalue,@outparam AS outputvalue', 
    N'@param1_from_sp_DB2 nvarchar(max)', 
    @param1 --Since this is the input param name from sp_DB2