Spermicides ARE chemical; the pill is a hormonal approach.
You have ignored the intra-uterine device. These got a bad rap twenty years ago when the Dalkon Shield, one specific product, caused many problems. The iud has been used for thousands of years in both humans and other animals. The natives of Taiwan have used pebbles from a "magical" stream for at least 1000 years. The local midwife did the insertion. Camel drivers on long trips inserted stones into the camels' uterus so she would be available the whole trip. The iud is still available; offers similar protection to the pill; is not noticeable during sex and needs little maintenance and is tolerated well by most women.
"Natural" methods were discussed here just last week. They range from looking at the calensar to rather sophisticated analysis of the mucous around the service. They are described by clicking through the saidebar on the opening page. Generally, practicioners are soon called parents. The simplest approach means blocking out about a third of the month; the best about a quarter.
There are herbal approaches. They are notoriously unreliable because it difficult to measure the strength of the dose when you are boiling roots. Many of them, including common kitchen spices, are not really contraceptives but are abortifacaents. They cause cramping of the uterus and expulsion of whatever is in there. There is always the possibility of damage to the foetus if you do become pregnant. You really do not want to be messing with this kind of home cooking.
I do not agree with Dancing Doc. Although I did use a diaphragm for a few years, insertion can be an issue - especially at first. There is a standing joke among diaphragm users about the spring sproinging and the thing bouncing around the bathroom. Hey, they are great and represented a major step forward when they became available in Germany in the late 19th century. They are still available and I still have patients using them. Their effectiveness is about the same as condoms.
Brandye