The goblets will "unsnap" from the canes, but try to only unsnap the top part of the goblet, not the bottom too. Doing just the top leans the goblet away from the cane and allows for straw removal without bending - they don't bend well as they are brittle being that cold, and will snap if bent too much. If you remove the bottom part of the goblet too, then of course it will no longer be supported on the cane, and can be difficult to replace without use of the Styrofoam box (qv).
If you anticipate any trouble, a Styrofoam cooler and some spare liquid nitrogen are useful to have, as you can pour the nitrogen into the cooler, and then work in the nitrogen, thereby not exposing the straws to the environmental warmth and damaging the sperm.
Do note that liquid nitrogen is -196° C (-320° F) and can therefore burn you, so caution should be used wen handling it or anything that's been in contact with it. Be careful and you'll be fine - don't be intimidated by it, but do be careful and sensible!
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