Aromatics International includes a recipe section with wonderful blends developed over the years. They recently added several new recipes for natural antibacterial cleansers: a hand cleanser and a hand soap (the soap is listed under colds and flu).
I find that when I clean with natural antibacterial cleansers and essential oils, I feel much better than if I used chemical cleaners.
Essential oils are well known for their anti-microbial effects–many possess antiviral, antibacterial and anti-fungal properties.
You can do a search on Aromatics International for these (or any!) properties, and get a list of relevant oils. Use the search field on the top right of the website, and enter the terms “bacterial” “fungal” and “viral” to get the best results. There are long lists of essential oils that provide these effects, so pick your favorites for cleaning and supporting your immunity at the same time!