Should a Complete List of International Dialing Codes Be Provided or Only A Subset?

I am designing a form which prompts the user for their mobile number. The platform is global and therefore the form should be able to accept any mobile number from any country.

Looking at this Wikipedia entry which lists all the international dialling codes I see there are some not so familiar entries should as

Cocos (Keeling) Islands +61 89162
Turks and Caicos Islands    +1 649
Globalstar (Mobile Satellite Service)   +881 8, +881 9

It is not very likely that the users who are going to use this platform will be living in these locations (the last one is not even a country but rather some telecommunication facility). However, this is not certain and some users may need to provide mobile numbers with these dialling codes.

How accommodating should the form be regarding these lesser know international dialling codes? I don't seem them on any forms on the internet I have seen. Is there a standard list that is typically used?