I jammed a deodorant cap into the entry hard

What goes into a vac hose enters the smallest part. The handle is designed to be a small reducer to prevent some blockage so the obstruction must back out. Do not attempt to use a sharp coathanger as you could tear the inside of t the hose and do not attempt to push the cover deeper as it will wedge tight. Your best bet is to draw this item back out with another vac. Sometimes bumping,( not smashing) the side of the handle against a carpeted floor area while doing so will help dislodge the item. Failing that you will need to open the handle itself.

If you look closely on this hose there are several small screw covers which will pop out with a pin to reveal hidden screws. Once removed the handle will open like a **** shell and then slide off the hose. The handle must be carefully aligned when reinstalling and the wire covers installed last, with the handle fully in place.
If all else fails and you must use a wire coat hanger, create a small 190 degree hook at the end so there is no chance of a sharp edge cutting the hose itself if pushed to far. Post back with results or if you need more help