From the photo of the tower’s shadow in this article, I have two further guesses about the relative heights of the viewing platform and the pointy bits:
At some time in the year, the building’s shadow will probably show the viewing deck height and pointy bit height, so they could in theory be triangulated
Due to the surrounding urban development, it looks wildly unlikely that the shadow will hit any surface it’s actually useful to measure it on.
It might not be legal to use from the viewing platform to the pointy bits, and it might not work in broad daylight, but a laser distance meter with ~50m range can be had for around $20 at the low end and fits in a pocket ;)
A sextant is much less likely to cause problems by interfering with other tech, though.
From the photo of the tower’s shadow in this article, I have two further guesses about the relative heights of the viewing platform and the pointy bits:
At some time in the year, the building’s shadow will probably show the viewing deck height and pointy bit height, so they could in theory be triangulated
Due to the surrounding urban development, it looks wildly unlikely that the shadow will hit any surface it’s actually useful to measure it on.
It might not be legal to use from the viewing platform to the pointy bits, and it might not work in broad daylight, but a laser distance meter with ~50m range can be had for around $20 at the low end and fits in a pocket ;)
A sextant is much less likely to cause problems by interfering with other tech, though.
They will in fact stop you from taking fancy laser measuring kit to the top of the Shard: https://www.youtube.com/watch?v=ckcdqlo3pYc&t=792s.