Think cold glass of iced tea on a hot, humid summer. Using chilled water in the radiators would have them dripping moisture all over the floor and still not provide good cooling...you need either a split system, or ducts. Now, you may be able to use a high velocity system which uses small outlets into the ceiling or high on the walls...these are much smaller than a 6" recessed light, and can almost disappear if done well (depending on the ceilings). Cold air at your feet is uncomfortable, and radiators only work well providing heat, which rises and causes circulation. Introducing dense, cold air down low does little to promote circulation of the air, so you'd end up with cold feet and a hot head.
If you want to get rid of the window a/c units, you need something with fans and outlets high enough to generate some circulation and equally as important, a way to drain away the condensate from the chilling process that removes the moisture from the air.