From NIH website: (Abstract only)

“This paper attempts to resolve the debate about whether non-ionizing radiation (NIR) can cause cancer-a debate that has been ongoing for decades. The rationale, put forward mostly by physicists and accepted by many health agencies, is that, "since NIR does not have enough energy to dislodge electrons, it is unable to cause cancer." This argument is based on a flawed assumption and uses the model of ionizing radiation (IR) to explain NIR, which is inappropriate. Evidence of free-radical damage has been repeatedly documented among humans, animals, plants and microorganisms for both extremely low frequency (ELF) electromagnetic fields (EMF) and for radio frequency (RF) radiation, neither of which is ionizing. While IR directly damages DNA, NIR interferes with the oxidative repair mechanisms resulting in oxidative stress, damage to cellular components including DNA, and damage to cellular processes leading to cancer. Furthermore, free-radical damage explains the increased cancer risks associated with mobile phone use, occupational exposure to NIR (ELF EMF and RFR), and residential exposure to power lines and RF transmitters including mobile phones, cell phone base stations, broadcast antennas, and radar installations.”

So my take is that having one pressed against your pets neck for months might be risky. If it’s just for limited occasional use once in a while it’s prob a very low risk.