This is what I bought to hold my HOTAS on an armchair for Elite Dangerous. I imagine they would be much stronger than what you suggested. https://www.amazon.com/dp/B00006RSP1/ref=sr_ph_1?ie=UTF8&qid=1466737211&sr=sr-1&keywords=industrial+velcro

But over the summer, I wouldn't trust velcro that is stickied/glued vertically. The adhesive would wear off over time and you'd have that basestation fall off. This is why screwed on mounts are highly recommended.