Keep your address off the wishlist entirely and share it privately with the one person sending the gift. Use a neutral on-list note only to start the conversation.
A wishlist set to Anyone with the link can be opened by anyone who has the link, so it should never carry personal contact details. Wishpicks doesn't ship anything, so you and the gifter arrange delivery directly.
Steps
Leave a neutral hint on the relevant wish, such as "Message me for delivery details." See Where should I write delivery information?.
Wait for the gifter to reach out, or check in with the person you know is sending something.
Share your address through a private channel you trust, like text, chat, or email, with that one person only.
Don't post your address in any reply, note, or field that ends up back on the wishlist.
A few details
Wishpicks has no delivery-address feature and doesn't handle shipping. The gifter buys at the store and arranges delivery directly with you, or you share your details privately. Delivery is always coordinated off-platform.
Don't count on the gifter's reservation note to exchange details. It stays hidden from you to protect the surprise.
You can limit who opens your list: set it to Invite only and invite specific people by email. See Is my address visible to everyone?.
For the bigger picture on how gifters reach you, read How will someone know where to send my gift?.