In thinking about what you wanted to accomplish, rolling up a waterproof strip in the awning probably isn't that big of a deal, but running the control wires may be. Where did you plan on having the controller? Because I am pretty sure you don't want to roll that up in the awing too and will want to install it inside somewhere.

With that said.... you can use a controller like this one and their hand held remotes. They are Zigbee based and if you only plan on having the two devices, you can bind them together without and type of automation hub or bridge. The will talk directly to each other via touch link. But if you plan on adding any more devices then you need a Hue Bridge because you will be creating a mesh network. If you do get a bridge, it can be unplugged and stored once the lighting and remotes are set up as the remote will send commands directly to the lighting. The Hue Bridge is not needed. So it's not like you have to have the bridge plugged in 24/7 for the lighting to work.

An advantage in going with Zigbee is you don't need line of sight for the remote to work which is common with the cheaper products you found on Amazon.

You are best off with 8 AA alkaline cells, giving 12V directly. This will give around 2Ah, depending on the cell type, so it will allow 5 hours of running at 400mA. You will also pay out a good deal less per running hour in batteries.

You can buy a decent battery holder for 8 AA cells, complete with outer covers and switch, at http://www.digikey.ca/product-detail/en/BK-6049/BK-6049-ND/3635122

Using 9V batteries, with a linear regulator, you are quite right in assuming that the current draw will be 400mA per battery, giving an hour and a half of runtime per pair. Of the 18V generated, 6V is wasted by the linear regulator, so efficiency is <66%, and a third of your expensively-purchased battery power is going to waste.

Assuming the specs listed are accurate, yes, an 8A power supply will be fine.