When you just have to go now!!
Not a very pleasant topic to talk about but when you need to go you need to go.
It is difficult to get a hygienic toilet at most markets in old Delhi.
One can easily spot stinky urinals for men at most wholesale markets as those markets are mostly male dominated. You can visit a restaurant in this area but toilets there are as bad.
Its better if you wait to get out of these markets to a cleaner place but if you have to go then please choose an Indian style toilet. They are more hygienic than western toilets. You can request the shop keepers to allow you to use their toilets but sometimes they refuse. Here is what Indian style toilets look like
When in New Delhi or even old Delhi you can go into big jewelry shops as they will usually have a clean toilet. In New Delhi markets finding toilets is not really a problem as there are many restaurants you can visit and they will all be mostly clean.
Things to carry- Please carry a sanitizer with you along with wet and dry tissues when you are at crowded markets.