sp_execute expects parameter '@handle' of type 'int'
I think you meant to use sp_executesql:

EXEC sp_Executesql @SQL, @Parameters, @SourceTableIN = @SourceTable, @TableNotExistsOut = @TableNotExists OUTPUT


And as JonSeigel pointed out in the comment, you have mis-spelled a parameter in your statement:

SET @SQL = N'USE [' + @DestDB + '] IF NOT EXISTS (SELECT 1 FROM INFORMATION_SCHEMA.TABLES WHERE TABLE_TYPE = ''BASE TABLE'' AND TABLE_NAME = @SourceTableIN)
BEGIN SET @TableNotExistOUT = 1 END'


That should be @TableNotExistsOUT.