The most obvious are sandwiches. You can make finger sandwiches very quickly, and they can have all sorts of fillings. You could also put salads together pretty easily, make mini savoury tarts or for pudding, some fruit tartlets. A fruit salad is also a good choice if you bring forks. Another option is to make some pasta, and then have it cold at the picnic. If you want to make your own drinks, try smoothies.
Pasta salads are always a winner! Plus mini quiches, or sausage rolls sliced into small sizes. Cupcakes are also a solid dessert that can be made fairly easily into a number of different varieties, while not requiring cutlery to devour them.
You can also opt for an Asian party pack - mini spring rolls, mini dim-sims, samosas, fish fingers, etc. Try going to the Central Markets around the Chinatown area - you will get the best value for your money and they will taste divine! :)