I have cleaned and repaired a lot of furniture. I have never worried about disinfecting it.
If the dresser is veneered, water or water-based products can lift the veneer. Use soap and water if, but only if, the veneer varnish is still good, and don't let water sit on the wood.
Turpentine or the modern non-smelly kind removes old wax, etc.
Then you can decide if more work is needed. If the veneer and its varnish are good, cleaning and waxing may be enough. Use stains to cover up scratches.

(If the varnish is not too dried out (some missing, and breaks up like rock candy), use a little varnish solvent and carefully re-spread it with a cloth. Takes practice. If the varnish is bad, remove and re-varnish or refinish (a la SRS post) with linseed oil and turpentine- I like that myself.

Follow cleaning, if veneer is rough, with fine sandpaper (on a block, or with sander if you have one) to remove roughness, but do not cut down the wood.
Deep stains are hard to deal with- bleaching, and re-gluing may be necessary, but a little discoloration adds character to the piece!

Take a look at this video:
http://www.ehow.co.uk/video_4418276_gluing-cleaning-wood-veneer.html

There are other good hints on the net, but be careful, some bad ones are also there.