Change rowguidcol property to a different column
First of all, the Table Designer is not the wisest of all software and probably does not choose the approach to change the table that you would expect.  The designer usually creates a new table, moves the data, then drops the original table.  However, based on your error the designer also may not be FILESTREAM savvy.  

But if you try it yourself through ALTER commands, you will see that SQL Server cannot alter a column to remove the rowguidcol setting.   See what happens:

ALTER TABLE TABLEName ALTER COLUMN Col1 uniqueidentifier DROP ROWGUIDCOL;


Gives the error: Cannot alter column 'Col1' because it is 'ROWGUIDCOL'.

Acknowledgements to Martin Smith.  I overlooked the ROWGUIDCOL operators, which are:  

ALTER TABLE MyTable ALTER COLUMN Col1 DROP ROWGUIDCOL; 
ALTER TABLE MyTable ALTER COLUMN Col2 ADD ROWGUIDCOL;


However, because of the involvement of the FILESTREAM the DROP ROWGUIDCOL command cannot be processed.

So, yes, you need to create a new table and move the data.