Singapore is a small country such that you can manage your trip on your own, but since the hotels provide only breakfast, you might be forced to have lunch and dinner on your own if you are on your own, The people are friendly and very supportive, but since the group consists of 2 senior citizens, its better if you go on a packaged tour, that way you get to cover more places and the main issue of transportation and food will be void.
Taking a tour package would be the best but do check out the places that he is providing and have a list of the places you want to go and then make a choice