Whoever applies for the card will have access to the points. If you can combine the points with either Freedom depends on how your business account is set up. I'm a sole proprietor so my business accounts share a screen with my personal accounts because I am the only account holder. If you are a corporation or LLC partnership the rules may be different. DIscuss it with your banker as they know the rules. I am sure they will understand your concern about being able to move valuable UR points around.
The Cash just allows you to have a path to convert the points to cash. The Classic does not have that path as it allows transfers to hotel and airline partners. Other than that they are same card, same bonus and same 0% period.
Have you considered each partner opening up an Ink card for the business? You get the Cash and they get the Classic. As business cards for same business you should be able to move points between the two card accounts as well as between your personal Freedom accounts. That would be my plan as you have the option to get cash back and use points for travel.
Also worth noting you could each wait 6 months after getting these cards and then apply for the other card (you the Classic they the Cash) and net the bonuses again as it's a new product. I'm not a point hog or anything, just pointing out what might not be obvious.
2x points categories are different on Cash and Classic. Cash = gas stations & restraunts, Classic = gas stations & hotels. Since you are getting UR points, it doesn't matter which card you have to convert to cash back.