The official IchiRuki symbol Pt. 4
Leaving aside the heavy meanings for the snowdrop, since they’re associated to death we can also draw a connection to Rukia, since she’s the only one to hold that special title amongst all the other shinigami present in the series.
Credit to ichirukiChinese on Twitter for the image.
And picking up on the literature bit I mentioned before, Snowdrop is the original name for Snow White and so we have this:
Making it obvious that Snow White is yet another title that Kubo granted to her in her bankai form. Very fitting, seeing how she covers everything in snow and ice, even herself, turning into a completely white version of herself as if she fused with Shirayuki, whose name by the way literally means "Snow White". I can feel a theory being born from this already but I'll leave that for another time.
Now, having clarified that the snowdrop is representative of Rukia it's time to analyze the next item on our list:
To start off the two swords we're looking at are both Ichigo's and yet one of them is actually Sode no Shirayuki. It's worth noticing that at the beginning of the series when Rukia lends her powers to Ichigo, the sword he carries all throughout the Substitute Shinigami arc is in fact Rukia's zanpakutō made bigger by his own insane amount of spiritual power. In case you don't believe me, here are the images:
The fist image is from ch. 1 when she's offering her powers to Ichigo. The second one is after her fight with Aaroniero in ch. 269 after falling in battle and Shirayuki goes back to its sealed state.
Now, this is Ichigo's sword during the first arc:
In order these are from ch. 1 when he's fighting his first hollow, ch. 5 when he's scolding Sora for trying to kill his own sister and ch. 55 when Byakuya finally attacks him after he trashes Renji.
If you pay attention to the guard of the sword in both cases, you'll notice that it's the same, therefore confirming that for a while, Ichigo wielded Sode no Shirayuki albeit in its sealed state.
The second sword is obviously Tensa Zangetsu that despite being later revealed as a creation of Yhwach by taking borrowed some of Ichigo's shinigami and hollow powers, it's undeniably a manifestation of Ichigo's power and thus a part of him.
That would mean that the swords used in the novel's insignia are Sode no Shirayuki and Tensa Zangetsu, Rukia's and Ichigo's swords. Why is this relevant? Well, that's all because of the meaning of the position they are in.