That is a very valuable set of wheels and tires. Please do not do anything to them except maybe the John Deere tire elixir and maybe a light cleaning and application of a light coat of furniture oil to the rims!
@Drosentreter , the JD spray doesn't hurt the wood rims; it actually rejuvenates the finish binders a bit.
A tip, when applying the John Deere liquid, do not spray! You will end up wasting a heap of it. Just pour a bit in a small bowl or jar and apply with a small piece of sponge or a paint brush. One bottle will then go a long way.
If the intention is to make the bike a rider than please listen to
@C M Gerlach Chris's post #13. The cost will be lower than the value you will lose by blowing those wheels apart! If you are budgeting, then find a pair of 28" English wheels to use until you can upgrade down the road or find an affordable wood rideable wheel set. Many of us have two sets of wheels for our bicycles; the cherished originals that are safely saved and the second rider wheels.
Good luck! Please post pictures of the tires and and bicycle for us to see. I am very curious as those hubs/wheels are sexy as Mr. McCauley would say!