The pull chain unit is replaceable. You can buy them at the home center and Walmart may even carry them for a few bucks. The guts on the inside hold the switch and has 2 wires. The chain and switch is inserted from the inside through the hole with a nut that goes over the chain and screws onto the chain switch to hold it. Use the same nut that matches your shroud.
The tricky part is getting the fan apart without making a mess. That depends upon the brand but it is easier to take the whole thing down to work on it.