is it okay for me to keep offering 'sips' throughout the day, can he survive on just a little bit of milk quite frequently, until he feels better/gets his appetite back?
Thats what i would do, just keep an eye on how long it happens for
Is he just not seeming hungry or is he screaming?

is it normal for them to lose their appetite if they aren't feeling well?
Yes it can be especially if constipated but constipation is extrememly rare if you are exclusively breastfeeding
will my milk disappear? i really cannot be bothered with expressing, i don't have anything to express into, ie containers etc... and i hate having to wash and sterilise the pump after each time... sorry a bit of a whinge there...
Who told you that you needed to sterilise your breast pump parts between uses? Unless someone else is using it, you should just be rinsing them thoroughly between uses on the same day, and wash well in hot soapy water at the end of the day, rinse thoroughly and air dry

To answer the question it depends how long it goes on for. Probably not, but you may feel like it has becuase at about 4 weeks your supply will start to settle down anyway so you may feel less full.

As for the doctor - do you think you should take him? It cant hurt.