Check the style used in each box. It is most likely "Normal". If you make the style settings in both docs the same for this style then it won't change when you paste between those docs.

If you don't want the style definition for Normal to be the same: Create a new custom style (based on No Style) where the good flowchart is. Apply this style to all the text in the boxes. Then copy the chart to the other document. Since that style doesn't yet exist in the target document, it will be created with the same settings as the source doc.

Also, I assume you put your shapes inside a 'Drawing Canvas' rather than a 'Frame'.

The hyperlinks may need to be reset after pasting into the target document - it is not clear whether they should be seeking a bookmark with the same name in the target document or the original document source.

I believe that doing the graphic in Visio is not going to solve your problem as you still have to get the hyperlinks going to the right place and I'm not sure how Visio could output the hotspots for you unless you are importing html.

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Andrew Lockton
Chrysalis Design, Melbourne Australia