I've just done a test in my simple office lab.
Are you trying to setup a Wireless SSID for clients, but want to keep them from seeing your AP WebUI, right?
So then, you could leave your Eth port(s) configured as Bridge to WAN in VLAN 4 if you wish or is what you use,
and define an Internal Subnet (any other VLAN) and DHCP scope, assign that to your SSID with Local subnet NAT
and Route to WAN, and these wireless clients get an IP from your 'other' VLAN, and should still get thru your internal
network to the Internet.
However, with this configuration, no, I could not prevent the wireless VLAN clients from being able to ping the AP's
IP address on the other VLAN/network.
Depending on your infrastructure switch/router, you might be able to create an ACL on your VLAN 4 that deny's
the Wireless VLAN subnet, from having HTTPS (tcp:443) to your AP's IP address...? My simple network can't
test that ACL.