It's perfectly acceptable for a male hamster to live without a mate for his entire life, and it won't negatively impact his physical health. The key to ensuring a male hamster lives without a mate is to avoid housing him with female hamsters, or to separate a male hamster when he exhibits signs of being in heat.

Many people choose to keep multiple hamsters together, but this carries significant risks. Hamsters are solitary animals, and housing them together often leads to territorial disputes and fighting, which can result in injuries. Therefore, the ideal approach is to house each hamster separately. A male hamster can live a happy and healthy life without a mate.
Benefits of Keeping a Male Hamster Without a Mate
1. Reduced Risk of Fighting
There are several benefits to not providing a male hamster with a mate. One of the main advantages is eliminating the risk of fights with other hamsters. To avoid breeding, male hamsters should be housed alone as housing them together could result in unwanted breeding. Adult male hamsters will often show signs of being in heat, leading to fights between males. So, not providing a mate and keeping a male hamster alone is the most reasonable solution.
2. Preventing Overpopulation
It's common knowledge that rodents reproduce rapidly. They often have multiple litters a year, each with many offspring. When housed together, hamsters will breed without limit, which leads to an overpopulation problem. You can end up with more hamsters than you can handle, which can be difficult to manage. Finding homes for all these hamsters can be challenging. Preventing breeding in the first place is the easiest way to manage this, and choosing not to provide a mate avoids these challenges entirely.