Hi there,
Firstly, what has to be done or another way is there anything wrong with the watch.
From personal experience I sent my fully functional Chrono Quartz to Omega for a service. I specifically requested a new black dial and matching hands as the luminous was quite flat.
$1400 dollars later I got my watch back with a new LCD display, analog 15 jewel movement serviced, cleaned and oiled. New crystal, new internal bezel, all new pushers and pusher tubes with new gaskets, new crown, new seals on case and crystal and new batteries.
In effect it was a new watch, I personally resurfaced the outer case back to it's polished and brushed factory finish.
So barring any problems with the mechanism and etc I would suggest you need new case seal. The pusher seals can only be replaced by purchasing new pushers and tubes or by reseating the pusher seals yourself (requires tools and knowledge). You could forgo the pusher seals but then the watch should stay well away from water or rain.
The Analog movement is cleanable but would need I think, an Omega Chrono Quartz familiar person to service it.
So, can't say what or where to send it. I guess you could ask Omega to service the movement and forgo the rest of the stuff, your choice.
Hope this helps,
Geoff