I'm assuming your car is 82-up. There are basically 3 different part numbers of switches.
It's actually your dimmer/wiper pivot switch. Your stalk goes into the slot, which controls your wipers when you twist the washer paddle or the wiper switch. The cruise switch is on the stalk, but its wire goes to the circuit connection under the steering column (exposed wire sheath that goes down the column separate from the dimmer switch rod/wiper wires). The turn signal portion of it is controlled by the metal dimmer/wiper pivot switch to the turn signal which, basically has nothing to do with this particular switch. I don't think it does, but cannot recall for sure if it does have a hole in the back or not. If you can, you can poke a rat tail file or similar in there to poke out the broken stem. You MAY be able to drill a small hole, but recall the wiring for the wiper stuff attaches back there so not sure what you may or may not run into if you did. But if you find you can, that's what I'd do rather than risk tearing up that expensive pivot. This is a complex part. So even if you can find one, you'll pay upwards of $100 and more for one.
Should you need a replacement, IF you have delay wipers (RPO CD4), you will need pivot switch assembly GM #7843683 or equivalent. Standard DS-817 is one aftermarket option. I'm guessing you have delay wipers because you have a tilt wheel. (Delay, tilt, doesn't matter if column shift or factory console). This is the only instance I can find that the same part number pivot is the same whether you have console or not.
Non-tilt wheels were not available with CD4 if you had a factory console. You could do it without a console, but that was the only way. For reference, if you got a non-tilt column shift and have delay wipers, you can get GM #7842716 for a replacement switch. (No tilt, no console, but have delay wipers)
But- you could get tilt and not get CD4 wipers.
If you have a tilt wheel but 2 speed wipers, factory console or not, you need switch GM #7843684 (column shift or factory console, tilt, no delay)
GM #7842714 is the non-delay wiper switch with console and without tilt. Standard DS-816 is your aftermarket option for non-delay wipers. (Factory Console, no delay, no tilt)
You must match up your switch to the type of wiper system you have. Confusing? Yes. But know your car.
Good thing is, even used, they used these same part number switches on GRUNCHES of cars of the era like F-bodies, G-bodies, B-bodies, etc. So a junkyard gem may be worth it if the j/y car still has a column in it. Again, know what the car has to match yours.
As far as the stalk- you can use any same year stalk to fit in any of your dimmer pivot switches regardless. They don't have to match. The switch itself determines your wiper positions. The delay handle just has the correct markings. Just saying.
For your own specific application here- Boils down to you will use p/n 7843683 if you have delay, 7843684 if you do not have delay wipers since you have a tilt wheel already. Console or not.
