Mine has 4 screw into the wall. We used large metal washers to keep the screws from biting into the foam. If it was a snug fit from floor to ceiling, you could probably just wedge it in there.
The problem with the velcro technique is the adhesives on velcro do break down over time, accelerated by heat. You might get a couple of years out of it in a cool climate, and if that's all you want, you're good to go.
RST