How can I install a faucet bidet if my faucet doesn't have a removable aerator?
If there are no usable threads on the end of your faucet spout, then, short of rigging something up with a piece of rubber hose and some hose clamps, you can't use that style of handheld bidet.
Instead, perhaps consider this type: https://rinseworks.com/product/abt-360-the-aquaus-360-handheld-bidet-for-toilet-nsf-certified-3-year-warranty
It connects to your toilet's water supply, rather than your faucet. Not only is this a more doable solution in your situation, but it will allow you to continue normal use of your faucet.