It needs to be a bit bigger, my spindle measures 7.3 and you would be at the very top of the taper. The spindle needs a small amount if clearance or it will still be a very tight fit. Hence me suggesting 6.5mm but a 7mm will also work(narrow end dimension), you will be working at the narrow end of the taper with that. Mine is 7mm and the reamer only goes in about 15mm when the hole is the right size. To be honest some of the cheaper reamers with a faster taper would be good enough for the job, something like this:
http://www.ebay.co.uk/itm/3-12MM-REA...cAAOSwMedZcT93