I guess it depends on the type of string and how friable it is, because undoubtbly the fish will have a nibble on it to. Then it also depends on if the string has any dyes in it or totally organic like a plain cotton (that more than likely is dyed anyway). You could try wedging the zucchini or cucumber on one end under a heavy piece of rock like some spare slate but that could be hazardous if the rock/slate moves or is bumped by boistrous large fish.
Am not entirly sure on the current methods used to make rubber bands but at least they are organic to a degree being (usually) made from the sap of a rubber tree (laytex), but again I am not sure what processes they go through to get the end product, apart from heating and possibly adding some dye to get other colours besides brown. Since the rubber band would only be in the tank a short time (although I have accidentally left one in longer than a day with no ill effects to the fish) I couldn't see it having a diabolical effect on the water stats or the fish health. A rubber band will naturally deterioate over time as well, and if you see one that you are using for the above application I would change over to a new one.
Alternatively go to your local op/ second hand shop and buy up on spare forks (they usually have a bundle sitting around) so that your not raiding your cultery draw.
Maybe the little spiked things that go in the end of corn cobs so you can eat the corn straight of the cob would work, if you can find a couple heavy enough to counter weight the zucchini or cucumber.