So I went ahead and got the slightly larger 185/65/15 tires today... and before I did, I tested my speedometer against a GPS, and I found that it was approximately 4% slow. When the speedometer said I was going 100kmph, the GPS said I was actually going 96kmph.
I thought this was because my tires were bald, so that the circumference of the wheel has been reduced... and that after I got the new larger tires on, the speedometer would actually be too fast...
But to my surprise, the speedometer is now almost PERFECTLY calibrated.
It seems like it's at most 0.5% off.