Can I appoint a foreigner as my kid's guardian?

There is nothing written in Guardianship of Infants Act that explicitly prevent you from appointing a foreigner as your kid's guardian in your Will.

HOWEVER, while this is recognized in Singapore, it may / may not be so overseas. There may be laws in that country which has a specific way / application where it comes to guardianship, or a certain hierarchy as to who will be the one taking care of the orphaned children.

The main purpose of the Will is always to best reflect the Testator's intentions which the Court(s) will generally try to follow. However, due to the different jurisdictions/legislation, what we recommend is that you consult the relevant lawyer / Will writer as well in that respective country, and especially so if the kid him/herself is NOT a Singapore Citizen.