Come on man, it's about fulfilling the spirit of the challenge rather than trying to rules-lawyer our way out of it.
Well, the only practical alternative would be some "Asiatic" power (surviving Golden Horde, surviving Timurid state, etc.). China was too far to control Western Siberia, Iran was too unstable and the Ottomans not quite suitable geographically.
As far as the "Western" candidates are involved, I don't think that any of them is realistic. Look at the OTL Muscovite conquest. It started from a very-well prepared base on a border of Siberia (Stroganov's "empire") and while the initial raid was spectacularly successful in the terms of looting and battlefield victory, during the next raid Yermak & Co had been completely exterminated by the natives. Real conquest took a long time and consistent allocation of the resources and, again, relied upon the established bases supported from the "center" (European Russia). Plus there was a consistent flow of the militant migrants (most of which ended up as the official "Cossacks" with the established organization and supply from the "center").
Two critical issues are missing from your schema: (a) explanation of what happens to the Muscovite state and (b) time frame. Without clarity on these subjects speculations are going to be too wild to make any practical sense.
If we simply assume that the Dutch or the Brits are managed to reach Siberia (as in "Siberian coast") via the North Ocean before Tsardom did in OTL, then the answer is simple: they would not be able to get the necessary numbers where they are needed for colonization of Siberia (and not just of a permafrost zone

or Novaya Zemlya discovered by Barentsz) and even less to keep them supplied, maintained, etc. over the long time even just because of a short navigation period, absence of the intermediate bases (inhabitable coasts of the White Sea had been inhabited by the Russians since approximately XI century) and probably absence of a real interest of settling there as well: the main and only reason for the Dutch expeditions of the XVI century was an attempt to find Northeast Passage. The same goes for the English expeditions of the XVI century: Willoughby expedition sailed to find the passage, the only surviving ship landed on the White Sea coast (its captain was summoned to the court of Ivan IV paving the way to the English-Russian trade) and 2 other reached Novaya Zemlya after which turned West and their crews did not survive a winter on the coast of
Kola Peninsula.