It's the device (i.e., sensor) that has to perform the exclude but it doesn't care what hub is setting the exclude condition. It sounds crazy but it works. So you will exclude "from" Hubitat and then include it to Hubitat.
That's not correct. Zigbee devices will need to be reset (according to manufacturer's instructions) before they will pair with a new hub. For most devices, it's usually a matter of holding a button or toggling power a number of times (10x for Sengled bulbs; 6x for Ikea bulbs; Holding power (or reset) for 5 seconds on most SmartThings sensors, etc).
As Eric mentions, this is known as General Exclusion, but I have read of some older devices still refusing to reset (old GE Z-Wave I think), so @killowatts' suggestion for a minimote or z-stick is good too if you run into one of those stubborn devices.
Old GE/Jasco switches and plugs are the stuff of NIGHTMARES to exclude and/or reset. I have one outlet in my dining room that I have tried for MONTHS to successfully pair. I finally said screw it and gave up. It's the only Z-Wave device with no parent hub. I'm sure it's lonely, but cutting the power to remove it is just too much trouble (the fish in my aquariums would hate me).
Yeah the Z-Stick was very helpful, allowing me to walk around and exclude my upstairs switches after one of my earlier hubs died (faulty power supply). A good little tool to have around.
I don't know how old they have to be, but my "old" GE non-plus switches only need one tap up to go into pairing/exclusion mode. Easiest devices I have on my network to get into these modes. Sometimes too easy as they can be excluded if accidentally used while I have the hub in exclusion mode.
Mine are the 12721 model and around 4.5 years old. I have 3 of them. I keep meaning to replace them with something better, but my aquariums are all on the same circuit as the smart outlets and every time I cut the power to those tanks, my sumps go all sorts of wonky and my fish give me dirty looks. So, in the wall they stay being all dumb.
I have 5 of these and they all suck. I tried unpairing them from ST to put into HE and finally gave up. You would be wise to just dump them for something new.
You are correct, my mistake. The Zigbee devices will require a reset if they were not properly removed from ST. This does not require a hub or stick, it's just the device's reset procedure.