It really depends on what you mean by short haul traffic, while SQ
does not operate any narrow bodies, they do have a significant short haul network to feed their long haul routes, take for example their 6 daily flights to Kuala Lumpur (45 min flight time on widebodies) and 8 daily flights to Jakarta (SQ is effectively the major long-haul carrier out of Jakarta, given Garuda's limited long-haul network), not to mention extensive schedules to Penang, Bangkok, Bali and even further afield to Manila and Hong Kong.
One also has to be aware that geographic distances between major cities in Asia mean that flights are generally longer, averaging 3-4 hours for a short haul flight, this is considered long if we compare it to Europe or North America where there are many more sectors at 1-2 hours. SQ
is also very strong in terms of traffic from Europe to the South Pacific (Aus/NZ); India to the US, via the Changi hub as well as 5th freedom traffic to N. America.
To cover the short haul routes and develop new sectors, there is of course Silkair, which covers the gaps with narrow bodies pretty nicely as well, so all in all, there is a pretty good feeder network feeding the long-hauls out of Changi.