I think it sounds like a perfectly reasonable thing to do - indeed, I would think it was a perfectly reasonable thing to do even if 10 or 15 years had passed.
As you say, you're not going in with any expectations and it's not like she's a romantic ex-partner where you might be massively treading on toes if you suddenly resurface.
She might rebuff you but is that worse than passing up on the chance that in fact she's delighted to hear from you and you're able to re-start your friendship? If you don't reach out, you will never know if there could have been a reconciliation.
And even if she rebuffs you and shows no interest in further contact, you will have had a chance to express your sorrow and regret at how your friendship ended and I think that will be a source of comfort to you and her. And you will know that at least you tried.
In my last few weeks at uni, I had a massive falling out with the person who had been my absolute closest friend throughout uni. Fortunately, social media wasn't a thing back then (the early 1990s) so we weren't able to compound things and perpetuate the bad feeling by blocking each other on social media and similar types of acting out.
Several months later we did get back in touch and we became friends again - it was a shadow over our friendship for a while and we were probably not quite as relaxed around each other as we had been but we were still both glad to be back in touch and on good terms.
But even despite that, it remained a huge regret to me that we had fallen out when we should have been spending our last few, post-finals weeks celebrating together. She and I discussed it very recently - I said how much I regretted it and she said the same. It felt good to have finally said it - even nearly 30 years later :).
So - no, it wouldn't be strange - it would be human and appropriate and, whatever the outcome, I think it is likely that you and probably she too will feel better that you've done it.