I think the edge of the valve will hit the wood table top and should separate at the keeper end but I don't see how you are going to grab the keepers when removing or replace them when reassembling. And because the valve moves at least till it contacts the table there may be even less room to move than appears. It doesn't appear to have enough room.
I don't have a picture to show but for removing valves I have two tools. I don't think either one is right for an Airhead and I use one for removing and the other for assembly. One is a large C-Clamp type which I have brazed a socket on the end to make the right size. The other is the KD type.