There's good reason why we shower and use deodorant - it's difficult to hide that smell (plus you feel better after one).
However, given that wasn't an option, there are a few key points. The smell is trapped mainly in certain areas on the body - key sweat points:
So if you want to reduce the smell, you want to target those areas. (Note, those are not directly sweat glands, but represent pores - some for hair follicles, some for sweat, but the two usually have some correlation.)
The body
As shown above, there are certain regions which sweat and smell more.
If you get a few minutes, go to a washroom and handwash some of the key things. You can't get a full shower, but it'll certainly help, and freshen you up.
carry a wash-cloth for this purpose, it'll make it easier than using your hands.
baby-wipes go a long way, take up little room, and disinfect as well.
Carry an extra can of roll-on deodorant (spray ones will get confiscated by security). Use on targeted areas.
The clothes
Sweat and dirt seeps into the clothing, adding to the layers of stench. Do something about this:
- Keep a spare shirt at minimum, which you can change to, and stuff your dirties inside an plastic bag into your carry-on.
- If possible, carry other spare clothes, targeting those that touch your skin first.
And as a bit of humour at the end, above all, do not try to hide smells by lighting a match on a plane. Heck, don't even take matches onto a plane!
Footnote: even if the general showers at the airport are out of action, if you have access to a lounge (or as in the case with some airports, can pay to get into said lounge), they may have showers you could use instead.