So the strong assumption that you are referring to seems to be where Hutter writes: "Assume we live in the universal multiverse u that consists of all computable universes".
Earlier in the paper, he assumes a deterministic universe, which would be quite a strong assumption, but later he just assumes that the universe follows a computable probability distribution.
The assumption that the universe follows a computable probability distribution at its most fundamental level of physics may still be a strong assumption while the assumption that at some higher level, physics is describable by some computable probability distribution may be a weaker assumption. Perhaps one should not make any assumption about the universe at all and instead make the weaker assumption that the modeling capability of science is restricted to computable models only, and therefore, alternative modeling attempts are futile, which would prove that the best we can hope to do is to follow Occam's razor, or so. This would then still count as a proof of Occam's razor.