I'm not familiar with Packard instruments, but it was about 1970 that most firms were removing all forms of asbestos. Regardless of the following, it's best to assume the worst when playing with old instruments.
Unless you have access to free asbestos disposal, the cost of disposal of asbestos waste can be quite high, so I would dispose of it in multi-layer rubbish bags, without bothering to confirm identity.
Unfortunately, due to distance, I will not be able to visit you in prison if knowingly disposing of toxic fibres is a crime in your location.
The greatest danger is inhalation of almost invisible fibers - of which asbestos is the worst, but silica isn't far behind - so you need to take reasonable precautions during disassembly.
You should wear a particle filter mask and gloves, and before disturbing the material, you sould put the instrument on a large disposable plastic mat/sheet. Fully spray and soak the insulation with detergent and water to prevent dust during disassembly. You should place all the white material into a thick plastic bags lined with damp newspaper.
Don't use power tools or fans during disassembly, and once disassembled, ensure that you thorough wipe all surfaces with damp, disposable paper towels, and toss them into the bag. Add the base mat and other items. Seal and insert the bag inside another bag.
For your information...
Asbestos is fairly obviously fibrous and uneven off-white material ( a bit like a white form of plumbers' hemp - but thicker and, when woven, it's like a heavy hemp sack structure ).
The glass fibre woven mats that replaced asbestos mats were shiny, much more consistent woven structure, and very tightly woven, like polyolefin woven bags.
The insulation is likely to be inorganic wool ( usually alumina ), and there were a whole range of therm hardboards used for structural applications ( such as holding detectors, fittings etc, some with asbestos, and some inorganic ( silica or alumina ) .
Please keep having fun,
Bruce Hamilton