Hamsters are fastidiously clean animals. They prefer to keep themselves tidy and won't willingly wallow in their waste. Dried urine on your hamster's fur indicates either a housing problem or a health problem. Depending on the severity of the problem, this could be one of the few times in his life when it's acceptable to bathe him, but you have to do so carefully.
Clean Him Up
Your hamster's skin produces its own natural, protective oils that help insulate him. Bathing your hamster like you would a pet such as a strips those oils from his body to a potentially harmful degree, not to mention a wet chill can kill him. If you're going to clean the urine from his underside, do so cautiously. Using a bowl of warm water and a washcloth or your fingers, gently scrub the urine-stained fur. If the urine won't come out with just water, use a dab of baby shampoo to massage it out. If that won't work, you'll have to gently cut the affected piece of fur off with a pair of scissors.
Clean the Cage
Hamsters will keep themselves as clean as possible, but in a dirty cage they're less able to do so. It's your responsibility to keep the cage clean. If his bathroom waste piles up, the floor of his home will become saturated with urine and it can stain his fur. Do a daily spot check of the cage and remove any visible waste, and completely change out the bedding at least once a week. Not keeping it clean is inhumane. It causes not just soiled fur but also potential respiratory problems and other health and behavioral issues.
Monitor His Urination
If your pet appears to be urinating frequently, keep an eye on his water consumption. Hamsters suffering from health issues like kidney problems may drink an above-average amount of water, and in turn will urinate more frequently and with less control. This is especially prevalent in older hamsters. Drinking more water than he used to could indicate a health issue.
Seeing the Vet
Have a vet check out any abnormal behavior, including excessive urination. Before your appointment, monitor the rest of your hamster's behavior for other possible symptoms that you should report. For example, sick hamsters may not move around much, and they may stop eating. A hamster who is typically sociable may be inclined to bite when you handle him if he is sick. Keep track of all of his abnormal behaviors so that you can give your vet a comprehensive report.