Short Answer : no
Long Answer: Unless your transformer is a multi tap design and has this already you cannot 'rewire'.
A transformer is a physical construction of windings that work with the magnet to 'transform', and that does not work in any kind of variable fashion. A mulittap is effectively several transformers in one.
If your product is available in EU/AU voltage as well as US voltage, chances are you can acquire a replacement to work in SG, though this varies from very simple jobs to pointless complex replacements . Quite often some power input circuitry is on the circuit board with the signal processing stuff, so any modification is finnicky. Also, it is not a case of going to Sim Lim and getting a replacement,
That said, several Marshalls, most of SWR, later Demeter, some Mesa Boogie, Alembic can be internally rewired, and I have done work to these. You may need the schematic from the manufacturer and thier cooperation varies, though I have not had any difficulty in my dealings.
If you are stepping down to run a power amp, you'd be better off getting a 220-240v version as your are probably carrying a fairly hefty tranny mainly becuase you need the ampereage, but if it is a preamp pr efx unit and you are using a Hefty step down, you are doing something silly. A preamp or efx unit has very low current draw,even valve or tube preamps, and you can use an inline lightweight step down tranny.