Congratulations on getting into the MMS program.
It does not matter where the funding is coming from as long as you have it. the requirement is not to bring/import money into the US (such as the Investors "E" visa) but rather ensure you can cover your costs of living/tuition and will not be forced to be on public support or be forced to work.
Very many students have applied to students based on no-cosigner loans in the past years. If anything, it may help your cause - you are trustworthy enough for someone to give you $100k.
So, do not be concerned about this point. Many MBA students have applied with little left in their countries (they quit their jobs, sold all assets, etc to attend an MBA program) and the immigration officers understand that. They also understand that there are MUCH easier ways to sneak into the US than taking the GMAT, writing essays, doing interviews, getting into the Duke MMS, applying for a loan, and jumping all other hoops