Current ratings of cable and fuses are a minefield of confusing information.
The cable rating assumes that it's in a bundle with no cooling and so is extremely conservative, it is actually capable of carrying vastly more than that figure suggests.
As a rough rule-of-thumb fuses will carry their rated current indefinitely, twice their rated current for about a second or ten times their rated current for about 15 milliseconds.
Adding up the estimated resistances for your wiring, connectors, relay contacts and a couple of cold tungsten filaments in parallel gives a total that might be as low as 0.15Ω. That means the initial current as you switch from low to high beam (or vice versa) could be 90 amps! A 10A fuse will cope with that for perhaps 20ms... probably long enough for the bulb filaments to heat up, but the fuse will only survive for a limited number of cycles. A 20A fuse is still more than enough to provide decent protection against shorts but will handle 90A for a tenth of a second.
Unless you have an independently fused circuit supplying another source of light, LED driving lights tucked below the fairing for example, I really wouldn't consider using anything less than a 20A fuse.