at first sight it appears more straightforward to not export the graphic, but just print it on your new printer. If the chart is selected when you invoke the print command, it will only print the chart and nothing else, at highest possible resolution.
I guess you tried this already and it did not work out. Next I would suggest to export the chart in question as an PDF file: Select the chart, then click ‘Save as’ and save it as a PDF file. It will only save that selected chart. You can then open the PDF file in your favorite PDF viewer and print it, adjusting the size to the paper format of your printer.
Note that this does not involve the XL Toolbox at all, but it seems to me that it is the best workflow for your case. Exporting to high-resolution bitmap files comes in if someone (i.e., a publisher) asks you to provide TIFF or similar files.
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