As for Pacific Coast - I guess, Dutch and English would fill vacuum. Later Japanese would join them. However, I doubt that even all three nations combined would be capable to penetrate North Asia all the way to Urals from their Kamchatka/Sakhalin bases.
But Western and Central Siberia... Muslim Khanates were too weak (and distant - in Bukhara case) for real exploration and colonization of vast cold wilderness.
Chinese were way too distant, also, although they could colonize Outer Manchuria (modern Maritime Province of Russia), especially with more reasonable policy of Ching dynasty towards Chinese settlement in Manchu lands.
Mongols are and were steppe nomads, unaccustomed to taiga.
There are no obvious candidates for conquest of Yenisei Valley, Yakutia or Taymyr. Without Russians, Siberia could well remain Siberian Natives' land till 19th century (as New Zealand, for example).