Lost ID as an International Student, Can I Use a Photo of It for Wine Pickup?

I’m an international student living in NYC (over 21), and I recently lost my ID card issued by my home country here. Right now, I only have a photo of it that includes all of my information. I ordered a box of six bottles from a well-known wine website and will be picking it up from a location that’s convenient for me on my way home from work.

I am aware I will get IDed when I go to pick up my order, but would they accept the photo of my international ID? Alternatively, I also have my college ID, but it doesn’t show my date of birth. Would that be sufficient as well?

I am also aware that I can just bring my passport, but it’s the same street where my bag was stolen, so I definitely do not want to risk that, as it’s my only way back home. I appreciate anyone taking the time to respond to this!