Nope. Every event you publish to sky relay is literally associated with your public key and stored on that relay.
Discussion
*any … not sky
Publish to, you know who else has information to what you published? Literally everyone else.
Details on what relays can see here.
the fact that with primal you are connected to the cache relay, so they can probably hide your ip, to the other relays
Everything you do on nostr is a published event from your public key. Everything. Literally everything. E-V-E-R-Y-T-H-I-N-G