Hello.
Your software can be done, but it needs 2 separate apps, one running on Windows, and an app that runs on an Android phone (or an emulator) to check if the numbers has WhatsApp/Viber...etc. These two apps then will communicate between them (via cable or wifi/internet as you wish) and do the job accordingly. If someone tells you he can do it without that then he's lying just to get money (or don't know what he is doing and he is blindly bidding), because there is no other way to check if a number is a registered WhatsApp, Viber or Imo number.
I can do you the two apps for $1.2k and in less than a week. I can guarantee you it will be professionally done: bug free, meets all requirements and as fast as it is possible for it to run.
I will also provide full source code so you can recruit other developers if needed to do future additions or modifications.
Also, 100k list is not huge for a computer, don't let developers fool you (I worked with data of hundreds of billions of records)
Best regards,
Amar.