I wanted to know if you know of a drain cleaner that will unclog my drains but is safe…

Most products can have the potential to cause problems if our cats ingest them or come in contact with them. Drain cleaners usually use very strong chemicals. They are usually very effective but I would be sure to follow the directions carefully and also keep your cats away from the sink until any cleaner is washed away and keep the cleaner out of reach. I have heard of some people using baking soda followed by vinegar for clogged or slow drains. An internet search may result in a recipe for this. Last but not least, certainly a safe way to deal with a clogged drain is with a plumber, no chemicals but certainly more expense.