How to (easily) open links received on iPhone in an iPad
Yes you can absolutely airdrop them from the share menu of both WhatsApp and Safari. It appears in WhatsApp if you hold on the message, not link, and tap forward, then you see two options, 1: forward, 2: share. Tap share. Keep the conditions satisfied, Wi-Fi, Bluetooth, visibility in Airdrop. Same iCloud ID is good to have, not necessary. 

Also, you can add it to the reading list and then open it on the other device after sync is done and then remove it when you're done reading. 

Personal Opinion: I have found  universal clipboard fairly unreliable to use. See support articles on Handoff.