Is it safe to swim on the fourth day of your period with out using a tampon?

No. It is rude and disgusting to go into a swimming pool without a tampon. Other people don't want to swim in your period. It would be like going into the pool with your underwear on. Other than that you can swim it won't do you any harm. There is no reason while on a period that you have to curb or not do any activity that you don't normally do. Having a period is part of daily life and millions of women have them every day. There is nothing special about it or you.