Upload visualforce page to Box as PDF

I have a visualforce page with a lot of images in it. I need to upload it to a Box folder using the Box API. I have tried converting it to a PDF and storing it as an attachment in Salesforce, and then using the Box Toolkit to upload the attachment to Box. However, the resulting pdf is too large to upload to Salesforce as an attachment (25 mb). I would like to be able to upload it directly to Box without storing it in Salesforce or on my computer first, but I'm not sure how to do that. Any ideas?