i was told by my diving instructor years ago that a womans period is "dead" blood and it doesn't attract sharks, they like fresh blood. My daughter in law went on the dolphin swim last Sept. with us and she didn't have a problem with the dolphins. I would tell the women not to worry.
Not a problem unless you are pregnant. The one time I was at a swim we were all questioned if we could be pregnant or not. We all answered no, but when we were swimming, the dolphins swarmed around one woman. We later learned that she didnt know she was pregnant, but ended up being pregnant! The dolphins tend to hone in on / scan the fetus of a pregnant woman (protect her) and other people are shunned, therefore not getting any interaction. Given that they are wild animals and unpredictable, they may try to hurt the baby, The main reason they wont let you swim if pregnant (if I recall right) is that they dont know what effect the dolphins' sonar has on a developing fetus. And yes there was a story about a woman giving birth with the dolphins on one of those baby shows the other day. She and some of her friends traveled to Israel from England to do it. They all swam around with the dolphins, and you could see them giving the pregnant woman all the attention. When it was time to deliver, they put the woman in a separate tank (warmer water too) so she could have her baby. The dolphins were next door separated by a clear window so they could see what was happening.
I've heard the main reason against pregnancy is that multiple heartbeats confuse, or otherwise alter the behavior of the dolphins. Never a good idea with a wild animal. Not sure if there are any real medical issues (i.e. sonar hurting a fetus).
Menstruation has no real effect on sharks or dolphins.