Lots of things! Starting with the options that require no forward planning:
Just lock yourself in the toilets for 10 minutes and wash your... smellier parts using your hands, sink water, soap dispenser soap and the paper towels provided. Yes, it's not exactly dignified, but no-one's watching (probably), and it's more dignified than causing your neighbour to put medieval plague doctor balm under their nose. Bit of water and soap on your hands, push or remove clothing far enough to reach your... various crevices, quick scrub, dry off with paper towels, bin the paper towels. If parents can change and clean babies in those things, you can give yourself a quick scrub
Ask an attendant if they have disposable wet wipes available, or "hand sanitizer wipes". Many if not most airlines do, and some even give them to everyone to clean their hands before or after eating (seems to be particularly common in Asia). Even those that don't do this will often have a small supply available on request: they're useful for parents, germophobes and people who are ill or travel-sick (as well as the self-consciously sweaty). Then lock yourself in the lav and use them to freshen up. This is a favourite item for "10 things you didn't know you could ask for on a plane" type list articles:
If you forget to pack your own sanitizing wipes, ask a flight attendant since they usually have them on hand.
Bring a spare t-shirt or equivalent, then choose an appropriate point during the journey to change (e.g. between connecting flights, after changing climates, or maybe after sleeping). It's always a good idea to have some clothes in your hand luggage anyway, in case your checked bags go missing or are delayed
Bring spare clean socks if you prefer to take your shoes off on long flights and there's a lot of walking before one of your flights (e.g. it's an evening flight and you can't change or shower before heading to the airport)
Bring a plastic carrier bag or dry bag so that after changing, you can wrap your worn clothes up while still locked in the toilet and not stink anyone out while stashing them in your bag
Bring chewing gum, and/or one of those travel toothbrush/tiny toothpaste sets, often sold at airports, sometimes not unreasonably expensive. For example:
Bring your own pack of wet-wipes, or a flannel and/or a small travel/gym towel to make the self-cleaning process easier and reduce any embarrassment of having to ask an attendant for one (though trust me, they won't bat an eyelid, they've see so much worse...)
Some stores sell "anti-odor" or "anti-microbial" clothing, which could be an option for a frequently-stinky frequent traveller - but it might just be expensive quackery