The last week of May is the last frost date in the UK, Avierose, but its just a guide - we've had frost on 4th June before, and I was living in your borough the last time that happened. Unfortunately, by end of May, it will probably not be flowering. They're not hardy outdoors here in the UK, and although the bulb benefits from being placed outdoors for a while in June and July, actually having them as a flowering plant outdoors is difficult. If your balcony was southfacing and in full sun, well sheltered from winds, I might have suggested you try hardening it off and see what happens, but I suspect what would happen is the flowers and foliage would shrivel.
More info here https://www.rhs.org.uk/advice/profile?pid=118
I do have a suggestion though; since the problem is because of pollen sensitivity, why not grow one of the double forms of Hippeastrum? Like other double flowered forms of plants, they have no pollen or stamens at all, especially the red or red and white bi colour ones (see Exotic Peacock as a variety, picture here http://cactus-spb.narod.ru/4.12.html), though some double forms of Hippeastrum do produce pollen at the edge of a normal petal instead, varies according to variety. White double versions often have petaloid stamens, often with pollen though.