Sustainable alternatives are something that can be researched, but I don't think the first port of call is to turn the magazines paperless. A huge amount of time and effort goes into the paper issues, which have already been reduced year by year, with collaborations between the two working really well to tackle different student topics. 

It's totally understandable to be worried about the cost and eco-wellbeing of the magazines, but it brings writers to both societies and is a prestigious part of why people want to work in journalism, or purely even to see their work in print!

The reason people get invovled with student newspapers and magazines is normally because of an interest in getting into print journalism. For those who want to get involved, it being printed is extremely important: it's not just a blog which anyone can submit articles to, it's a physical thing which can form part of a portfolio to present to future employers or at interview. Having worked in this area before, I guarantee that the print copies of these publications will receive more attention than any online version or website ever could - so why take it away from those who want it and need it? 

If the worry is cost, then there should be a greater effort by the student union to find sponsorship and advertising revenue (this is exactly what other student publications do and there is a huge potential to earn a lot of money this way) or being smarter about the number of copies printed and where and when they are distributed (apologies, I don't know the full details on this and it's possible this is already being done!).

If the problem is the environment, then move towards more environmetally friendly and recyclable papers and encourage those involved to ensure that any leftover copies are recycled when they are removed.  

The feeling and enjoyment of holding something you are reading would be taken away if this happens- I hate reading on kindles because I prefer holding books- We can improve the environement in different ways, like using recyclable paper, encouraging more online reading, rather than going to the other extreme and disallowing it altogether. 

I think you're picking the wrong battles. Making papers increase their reach and engage students who don't take the effort to follow them online. Engaged students are probably more likely to care about things happening around them.

More efficent fights:
SUSU still uses a lot of plastic in the shop. Not an easy fix, but big impact.
Encourage sustainable diets. Veganism/insects/reducitarian...
More plants.
Email local MPs about things