You can use any surfactant (preferably anionic, with amphoteric and non-ionic) to create a liquid handsoap. The choice is yours. And it will be even milder as the pH will be more skin friendly.
You can you SCI, however it is a bit tricky to work with. It is better in “bar” formulas.
Hope this helps?
This is exactly the kind of answer I was looking for, thank you!