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:

![enter image description here][1]
[(source)][2]

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][3].  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.

  [1]: https://i.sstatic.net/z3GLV.png
  [2]: http://io9.com/5984591/you-probably-dont-know-how-many-holes-are-in-your-body-right-now
  [3]: http://www.dailymail.co.uk/news/article-420815/Flatulence-grounds-plane-passenger-lights-match-hide-smell.html