Is it rude to decline an offer of "lunch money," and instead ask to reschedule?

Actually in most polite societies it is deemed polite to decline a gift the first time it is offered. In Japan for example it is considered polite to reject the gift twice and not accept until/unless it is offered a third time.

In this particular instance it all depend on how you word your rejection of the offer. If you were to say:

"Keep your money. I'll just wait for a better time."

It could be considered rude. However, if you were to say:

"Thanks for the offer, but I think I'd rather take a rain-check and have lunch with you some other time."

It is more likely to be better understood, and better received.

I think you have answered your own question. It is definitely not rude to put it like that. If anything it is a little rude to take the money without going to lunch with her lol

I would graciously decline with "Oh, that's alright, I'd prefer to wait until you're feeling better and go with you." Not rude, in fact, it's far more polite than taking the money.

It's always rude to decline a gift, you'll have to be very careful with the wording.

properly you may want to attempt, yet they're in all likelihood fairly dry and they'd be somewhat not basic to get down... particularly the filters :P Hardcore non smoker. My grandmother died from emphysema and my perfect pals mom from lung maximum cancers, i have been a ideas to heavily linked with the repercussions of smoking to ever imagine of doing it myself.

I don't think it would be rude at all. In fact it's more of a compliment.

Not at all. I would, however, wipe the brown stuff off your nose before returning to work though.

It's not rude at all :)

I think that's very nice and would certainly please her.