Router -> Bridged GS752TP & GS724TP -> LAN & Isolated WAP

Hello, I have a complex setup that I'd like assistance with.

Internet <-> Gateway (Firewall, DNS, DHCP) <-> GS724TP <-|-|-|-> GS752TP <-> WAP

The two switches are bridged (4 ports truncked w/ Cat6). Each switch has many other devices plugged in.

I'd like the WAP (wireless access point) to be isolated from all of the other LAN traffic (on both switches), but be able to access the internet via the gateway. Can I do this without an additional (hardware) firewall between the switch and the WAP (blocking all other non gateway, local traffic)? I'd like to avoid a double NAT stuation if possible. 

Would I be able to setup a VLAN for a single port on each switch to accomplish this goal?

WAP <-> VLAN Port on Switch52 <-> VLAN Port on Switch24 <-> Gateway <-> Internet

I guess in this case I'd run a 5th Cat6 cable between the switches (separate from - but in addition to - the 4 trunked ports).

Would this work?

Thank you!