No, it is not possible to change the country of residence for the Shopee App.
If you want to view or purchase products from other countries, you will need to download the Shopee App specific to that country (e.g., the Shopee SG App for Singapore).
Here is how you can change your Google Store/Apple ID region accordingly to download our Shopee app,
Android : Official Google Play guideline
Apple : Official Apple guideline
Once you have downloaded the Shopee App for that country, sign up for a new account using a locally registered phone number to start shopping.