Practical English Usage 124.5 offers
We often use can when we offer to do things for people.
Can I carry your bag? (= Would you like me to ...) ~ Oh, thank you.
I can baby-sit for you this evening if you like. ~ No, it's all right, thanks.
Could is possible if we want an offer to sound less definite.
I could mend your bicycle for you, if that would help.
PEU says could makes an offer sound less definite, but in which way? Does it mean that the speaker is not quite willing to help, or he is not confident in his ability to deal with the trouble, or he is just showing politeness as he doesn't know whether his addressee really needs help, or any of them depending on the context?
I know could sounds more polite than can when used to make a request, which is borrowed from the hypothetical use of can, but I'm wondering if I can say "Could I carry your bag?" or "Could I mend your bicycle for you?" to make my offer sound more polite.