Using small images with pretrained models?

is it possible that I resize the pretrained models to work with smaller images (40x40) instead of 256x256? I want to try decreasing training time by first doing my experiments on smaller images (40x40). Is it even possible to take a pretrained network and change it to process 40x40 and then fine tune on top of that? Are there any other issues with doing this? And if its possible, how would would go about doing this? I read all the docs on pretrained models and didnt see a lot of information.

all the pre-trained models require 224x224 images as input atleast.
If you have smaller images, you might have to upsample to 224x224.