Hi Lew, welcome! Sounds like you've got a good background and skillset for this.

Re: spinners, as mentioned they can only be run in a few arenas, two of which are at Extreme Robots events and RoboDojo events. There is also the Robo Challenge arena and they tend to host events around the Birmingham area, however it's been a few years since their last event and not sure what, if anything, they have on the cards for this year.
With testing, it really just comes down to common sense and an awareness of health and safety. Don't stand too close, don't stand in the same plane as the spinner, use safety devices (i.e. locking bar) when arming up and deactivating, and a pair of safety goggles won't go amiss. If you have a piece of steel or polycarb you wish to stand behind, feel free. Also make sure the surface the robot is on is stable; if there's any vibration or wobble in the spinner, it could cause the robot to oscillate or bounce, which in turn could make the spinning mass connect with an uneven surface. I'd only worry about a test box or inspection pit if you want to run the drive at the same time as the weapon, as the gyroscopic forces could also cause the robot to tip or tilt, potentially sending the weapon into the ground too. If you're just testing the weapon on its own, a safe distance will be fine, maybe with a camera and tripod set up closer if you want to get some visual data.

Re: hydraulics, there are more arenas you can run them in however be aware that some roboteers may ask you to hold back from fully crushing their robots at non full-combat events as they don't generally expect to take large or expensive damage at these events. Hydraulics are very limited in the FW class - Pressure Point as mentioned, and Cobalt (not the Battlebots robot) - due to the weight however that rarity makes them more exciting and interesting when they do appear, and since you've got the background, it would be great to see one. A hydraulic crusher will also be easier/slightly safer to demonstrate to friends, work colleagues etc compared to a spinner.

Best of luck with whichever you choose (why not both? )