Things are always harder to put back together. Besides, that would probably kill the warranty.
Your cell phone has a lot of little openings. And it's an advanced electronic device. So, it's important to keep it as dry as possible. Creating a short would be easy.
You're cleaning plastic and possibly an LCD screen. Abrasive cleaners would scratch either. Some chemicals could either scratch or fog them. I'd avoid most commercial cleaning products.
LCD screens on phones are often covered with plastic. A commercial cleaner might damage that, too. I'd prefer not to take the chance.
Instead, I'd use that all-purpose cleaning solution, isopropyl alcohol. Remember all those little openings. Make sure your phone is turned off before attempting to clean it. You should also remove the battery, if possible. Then, wet a cloth with the alcohol. You want it damp, not sopping wet. Work fast; alcohol dries and evaporates quickly. You'll probably be OK if alcohol squeezes past the keys. But I'd be in no rush to find out.
When wiping the phone, hold it upside down. This may not be necessary, but I'd rather be safe. Make the liquid work against gravity. It will be less likely to get into the phone. If the phone is truly dirty, use cotton swabs. Sometimes goop accumulates around the keys. You may also find it around ports. In that case, dip a cotton swab in alcohol. Shake as much out as possible. Work the swab around the opening.
If necessary, dry the phone by placing it washed side down. The alcohol should dry quickly. Don't place it over heat; that could damage the battery.
The type of cloth you use is also important. It needs to be soft. So, I'd go for microfiber. You should be able to find that in stores. It's also available on the Internet.
Paper towels are a no-no. They can include tiny pieces of wood. They won't look so small to your phone. The result could be scratches.