Konstantin,
I have a copy of the afore-mentioned "jewel book" (The Jewel Album of Tsar Nicholas II) and have looked through it in order to find the items that you have mentioned. I couldn't find a gold ring, but there are two gold crosses shown.
The first, listed as No. 20, has the earliest date recorded in the book, and the inscription next to it reads: "From Apapa. 1879." "Apapa" was Nicholas's maternal grandfather, King Christian IX of Denmark. The book notes that this is "a six-pointed cross." The second gold cross, No. 33, has the following inscription written next to it: "From Uncle Paul and Alix. 4th June 1889." Grand Duke Paul Alexandrovich was the youngest son of Tsar Alexander II, and Alix was his wife, the Grand Duchess Alexandra Georgievna. This cross was received as a gift on the occasion of their wedding.
If you'd like, I can e-mail you a picture of the pages in the book containing the drawings of these two crosses to see if any one of them is the one your grandfather was given. However, keep in mind that Nicholas only recorded the jewelry he owned in his jewel book until the year 1913. So if they do not happen to match, even though it would be harder to prove the claim that it actually belonged to Nicholas, it would still be possible if he received it after 1913 and thus went unrecorded.