if by green zones, you're referring to like check points, or some type of area control, that could be seen as field work - chances are this would be for an MOS 31A for Army - Security Forces for AF - not sure of the job codes for other branches.
Your PT for that MOS wouldn't be too taxing in basic I wouldn't think, and probably wouldn't be any worse in AIT. I know the APFT has changed dramatically per job, but I wouldn't consider it taxing. I would be confident in saying that you'd more than likely have an issue with 11X (11 series is light infantry X is a placeholder for specific job) over any other MOS with asthma.
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