Urethane and poly-urethane are very different things.The mold and all would not be too difficult to make - as long as you have a good understanding of injection molding.The injector would be a bit more challenging,but most of you creative thinkers could conquer that.The hard rubber would be the problem.The RTV compounds that are used for molds are too soft to make handles from.You could try some sort of resin,but that is not the same ad rubber.There are some thermo-plastics that would work,but they require pressure vats to melt them and inject them.Air bubbles are going to be the biggest problem,without big industrial injectors.
An alternative would be to use sheets or blocks of hard rubber (easy to get ) and make a two piece mortised handle or a stick tang and block handle.Vulcanizing the two sheets together would be fairly easy.The supplier should be able to sell you the vulcanizer.There is a thick black compound that Ken at K&G sells called Epoxy-Patch (part # EP11).It would work good on a stick tang insertion in a block of hard rubber. You might even try it for injecting.
The final thought to consider is that your injector is probably going to be a one use device,since the injected compound will harden in it,too.The cost to make one handle could be $50 to $100,maybe not cost effective.