Used Pan.... Old Oil.... Can this pose a risk before washing?

It is highly unlikely that your pan will pose danger of botulism.

The botulinum bacteria doesn't live in oil, it lives in plant matter which is cut off from air. This is why storing plants (garlic, spices and the like) for a long time under oil is dangerous. But the oil by itself is not the medium in which the bacteria can grow, it is only needed as an airless buffer between their actual medium (the plant) and the environment.

Even if you had fried plants (e.g. potatoes) in that oil, it wouldn't have been much of a problem. The bacteria's spores can easily survive home canning temperatures, but they are only slightly higher than 100 Celsius, even in a pressure cooker. But when you fry in that oil, you use at least 180 Celsius; in my experience, home cooks (myself included) are prone to letting the temperature get a bit too hot, frequently over 200 Celsius. Combined with the fact that any crumbles left after frying are probably charred, so too low moisture to support the bacteria, I can't imagine a colony establishing itself.

Lastly, the toxin itself is much easier to destroy by heat than the spores. In the very unlikely event of contamination, the spores will die on your sink and other dishes, because they will be in contact with air. If you are still nervous, fill your sink, together with the dishes, with just-boiled water. The toxin itself is neutralized after 10 minutes at 80 celsius.

Botulism is one of the least likely results here. The bacteria are obligate anaerobes, and will grow extremely slowly or not at all in an open pan.

This doesn't mean that there aren't plenty of other bacteria which will compete in that environment, especially if there are any bits of food left over. I certainly wouldn't cook with that pan again before washing it, for example.

As far as contaminating the sink and sponge: sinks, sponges, and dishcloths are disgusting. They are surprisingly common sources of cross-contamination and general food-related illness in home kitchens. They harbour not only bacteria but also various molds. This rarely causes fatalities but is frequently responsible for the typical stomach aches, diarrhea, and other minor symptoms that people tend to incorrectly attribute to restaurants or whatever they last ate.

I'd have a hard time believing that washing a few-day-old pan could make your sink or sponge any worse than these things already are. You have to consider that sinks and sponges are wet environments and bacteria can grow in or on them almost as easily as they can in your used pan. Studies like the one linked above indicate that dish detergent will help reduce some, but not all bacteria in sponges specifically.

The bottom line is that you should be replacing sponges and tea towels and disinfecting your sink regularly anyway, especially if you've recently been working with anything likely to be contaminated, such as raw meat. If you don't do this regularly, now's as good a time as any to start.