so long as you don't have much draw from the midspan that fan should be fine and way quiet. I suspect that it will not be sufficient to cool it when more than about 100W of PoE is asked for and delivered. What you need is a used 1U (40mm) server fan from an excessed rack mounted server. If you don't have any local stock of that sort of thing,
ebay is your friend. I used to have a bunch in my garage, but tossed them a couple of years ago. The one caution i want to add is this. If the midspan does not control the speed, the higher powered server fans will drive you crazy with the noise. I suspect that the midspan does control the fan, however, but you still shoudl get one with a similar speed/power curve. The Delta fan that i linked to should fit that (just an educated guess YMMV).