Ok other methods described here are awesome like
Inserting a straw into it and measure the number of clicks ( the clicks can be recorded and time difference between the clicks can be measured using a audio editing software )
Tie something to the end of it and measure the angle it makes with the vertical and measure the velocity by using the relation
$$ (\omega)^2= g*tan(\theta)/r $$
My method may look far-fetched but in theory it should work ,It uses Probability to measure the speed it is basically a Monte Carlo experiment where you calculate the probability of an object hitting the fan both theoretically and and practically by actually throwing lots of shots.
A fan has 3 wings each of them has an arc length of say 20 deg if we assume the fan to be stopped (at random places ) then the probability of hitting it will be 60/360 but if the fan is moving say with speed of ω and object remains in the plane of the fan (the vertical position in which object can hit the fan ) for time T seconds we know that
$$ \omega= d\theta / T $$
now the fan will behave as if each of its wings are having an arc length of
= 20 + dθ hence making a total wing area of
$$ AREA = (20+d\theta)*3 $$
probability of hitting the fan becomes
solving it for ω
where p(hitting) can be calculated by actual throwing for example if 30 times you hit out of total 100 throws p(hitting) becomes 3/10 . Though you will need to make those throws coherent and do a reasonable approximation for T .
I have described the method here