Is it possible to configure an iOS device to remember credentials for a Wifi SSID but NOT auto-join it?
There's isn't a great solution but one possible workaround is to set SSID A to use a non routing static IP and just switch it back to DHCP whenever you actually want to use it. Just click the circled i to the right of the network name and click the Static toggle.

You'll need to enter a valid (but non functional) static IP and Subnet Mask (I tested with 10.1.1.1 and 255.0.0.0) or it won't keep the static IP setting. This let's you keep wifi on all the time and never enter your password again.