Yes, you are slightly thinking about this the wrong direction
In general, except when dynamic routing protocols are in use, each end-device (host) on a LAN will only ever make use of *one* router for reaching other destinations. Routing is an active process, not passive, so the layer 3 switches can't just decide to route some packets and not others, they are asked to route packets.
A VE interface is necessary for routing on that device, but the presence of a VE interface won't (alone) cause any routing to happen. Hosts have to send packets toward that VE interface for routing to happen.
So, in your scenario you should decide which of your two ICX devices you want to handle routing of traffic, and leave the other one configured for just switching. The one that handles routing doesn't have to know about *all* routes in your network, it can route traffic upstream to your other router, but it can certainly handle routing between your VLANs.
If you want every port on both switches to be layer 3 (routing) enabled, you can stack the switches so they become a single logical unit; with that in place, any traffic from a host that needs to be routed to another host on the same physical unit will stay within that unit. Stacking can add a lot of complexity though and upgrades are more difficult, so it's not something you want to do without being ready for it.