There are two ways to do it.
1) check whether just amend the date of SIN-PER and PER-LHR and what are the price difference. You can buy separate ticket for SIN-Phuket with SQ or other low cost carriers


2) check the price difference if need to add in SIN-PHuket-SIN and change of date.

but guess the lowest fare class are already sold out, so the price difference will be big