Hi Oldowl
I don't know about walking tours I'm afraid but there is a lot you can do in 3.5 days! I can recommend the following:
Walk along the river - Start at Robertson Quay, through to Clarke Quay, Boat Quay and to the Merlion. You'll see a lot this way and spectacular views towards Marina Bay Sands when you get to the Merlion.
Gardens by The Bay. Pay extra to go into both of the Domes - especially the Cloud Forest.
Botanic Gardens and the National Orchid Garden (small fee to enter)
Go to Sentosa Island. Can do this via cable car from Mount Faber if you fancy.
If you like walking, google the Southern Ridges tree top walk.
Go to China Town and Haji Lane for a wonder
Visit a local Hawker centre for a bite to eat. I can suggest Lau pa Sat (and from 7pm Boon Tat Street opens up with lots of Satay Stalls for dinner) or Maxwell.
Night Safari - good fun for a solo traveler. Or the Zoo.
Have a great time! It's a wonderful City!