I think everyone seeing who you zapped on Nostr it's no different from seeing notes that you liked, I think its harmless. Custodial LN wallets like WoS can see your txs but they don't know who you are if you are a nym in Nostr.
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It's not dependent on your wallet, but rather your Nostr client.
You want a Nostr client that allows you to submit anonymous Zaps, like Damus. Otherwise you can send someone a regular, non-zap tip but clicking the lightning address in their bio.