wireless router can do what you want, I’ve also experience configuring netgear.
Try to do this sir:
1. On your netgear WAN port, configure an IP address which is on the same subnet as your wired network.
2. On you netgear LAN side, configure your wireless LAN subnet range <your NETGEAR will serve as your DHCP server> so that all wireless client will obtain an IP address which is or should be on different subnet as your wired network.
3. Wireless Routers use NAT to translate its wireless network to your wired network but in your case, proxy is not configured to your wireless clients, if it is possible for you to configure it on your NETGEAR, much better, if not, you have to manually set it just like on your wired network.
**For testing purposes, try ping tests from your wireless to your wired network before adding proxy settings.