You have one in your own question: nitric acid. It's not hypergolic by itself, it's really the combination with hydrazine that's hypergolic†. You can in principle use nitric acid as an oxidiser for less dangerous fuels. Nitric acid is still a very dangerous substance though, so there's not much point.
The most important liquid oxidiser that is relatively harmless is hydrogen peroxide, which was indeed widely used in early rockets. It is not very efficient though (low specific impulse), which is why it has largely fallen out of favour for space applications.
Obviously all good rocket fuel combinations are reactive, that's the whole point. The best you can do to make it safe is to use something with high activation energy, but this activation energy is basically subtracted from the total energy you can get in the end. Hydrocarbons are a remarkable exception to the dilemma, based on the fact that carbon can form stable molecules although neither the C-C nor C-H bond is so strong to make this energetically unfavourable. This could be considered a nanoscale version of the same principle that also makes solid fuels safe: the grains of oxidiser and fuel are physically separated‡, and only when reached by the flame front do they properly dissolve and are thus able to propagate the combustion.
So, what you seem to be looking for is an oxidiser with large, stable molecules involving fairly weak bonds, like kerosene, which is nevertheless liquid. I don't think such a substance exists; the problem is that all the elements with suitably high electronegativity have unsymmetrical bond geometries, badly suited for forming stable molecules¶. Sulfur is perhaps the closest thing to fulfilling the criteria, but it's only liquid above 115°C and a pretty poor oxidiser. Then you could as well use cryogenic oxygen.
The holy grail of efficient-yet-safe rocket technology would be nuclear fusion, based on the fact that it has both much higher energy output and much higher activation energy. Unfortunately the activation energy is so enourmously high that we're still far from being able to get fusion fuel to react at all, on a scale that would make for a usable rocket.
†Generally the term "hypergolic" doesn't make sense for any individual substance, it's always a combination of at least two that acts hypergolically. Oxygen could also be considered as hypergolic since it spontaneously reacts with pyrophoric fuels such as triethylborane.
‡Liquid-fueled rockets of course also use physical separation as their primary safety mechanism, though on a much larger scale.
¶That is, stable large molecules. Nitrogen forms, in addition to many unstable oxidiser compounds, also the extremely stable N2 molecule – but its stability is based on the single very stable triple bond, which makes it completely unsuitable as an oxidiser.