The best I can tell you is, if you're going to restore the Honda, yes, use the old tires. Know, however, that they will no longer be usable. Riken tires were gum rubber based, with only trace amounts of butyl rubber added to extend the life of these tires to about 4,000 miles. Difficult to find at best.
If you are actually going to ride it (which I recommend) then put on new Dunlops or Avons. Since your Dream has mechanical drum brakes, double check them and then check them again, as Honda used asbestos linings. Upgrading to ceramic linings will not be visible, and will DEFINITELY give you better control and stopping power.
The Dreams all had knee shocks in the front, which gave riders control problems, especially on slick roads and expanded steel bridge decks. My advice is to park it, start it once a month, let it come up to operating temperature, ride it around the block a couple of times, and park it again. Double check the final drive chain, as they are known to stretch. The rear sprocket will tell the tale. If the teeth are worn, replace it, if you can find the part. That is the bad part about ricers: they never keep parts in stock.
If you just let it sit, it will definitely lock up on you. Sadly, the chances are bad that it has already locked. To unlock a frozen motor, pull the plugs and fill the cylinders with diesel fuel, then wait an hour or so for the diesel to soak its way through the (probably rusted) piston rings. DO NOT USE WD-40 or Marvel Mystery Oil. Avoid STP! Push the kick starter through GENTLY to loosen the pistons from their entrenched place in the cylinders. Then change the oil and filter to remove the diesel. Refill with 10-40 paraffin-based oil: that vintage Honda will not take kindly to synthetic oil. Then, check the actual compression with a pressure tester: look for at least 100 PSI in each cylinder, +/- 3 lbs. If you are out more than that, you're into a top end rebuild.
