--- No, you should use a fuse which blows (or a circuit breaker which breaks) if the steady-state current into your load is exceeded for some amount of time.
ISTR that your fan dissipates 60 watts, so the current it needs from the mains will be:
P 60W I = --- = ------ = 0.5 ampere E 120V
However, the inrush current could be up to 10 times that high, gradually decreasing to the running current as the motor comes up to speed. Which could be a problem if you don't let the motor run/rest long enough per ON-OFF cycle to get rid of the extra heat generated during startup.
In any case, if that turns out not to be a problem, I suggest you use a slow-blow fuse:
Take a look at the chart on the bottom right of the page and you can see that a 2 amp fuse will carry 5 amps for 7 seconds before it blows, but then it also has to cool down, so you may need an electronic solution.
Before you get into that though, I suggest that you run the thing with various duty cycles for long enough to determine whether the motor will overheat.
-- JF