There's a product that they use to remove surgical adhesive - it comes in little individually wrapped swabs - can't remember what it's called but you should be able to get it from a pharmacy. I remember getting an awful reaction (ie: blisters) from the adhesive in the surgical dressings after my c/s, I wouldn't usually use products like this on my skin but the longer the adhesive stayed on my skin the worse the reaction. It stung on the blistered areas (not surprisingly) but was quite gentle on the rest of my skin.

I'd be cautious with eucalyptus oil neat on the skin at the best of times, but on sensitive post surgery tissue you might be inviting irritation.

Actually, that reminds me - my grandma had breast cancer and had a mastectomy - I'm not sure if she also had chemo or radiotherapy, but I think she did. Since then she's had incredibly sensitive skin and can't use anything but hypoallergenic products on her skin. She can't use anything fragranced, whether synthetically or with essential oils. Apparently this is quite common with oncology patients who've undergone radiotherapy or chemo, so it might be something to be careful of.