Hi okay - sorry I'm in Italy so I've been out of touch otherwise I would have weighed in before now. - YOU DO NOT WANT TO WAIT! Sorry - this cancer can be VERY aggressive particularly in young people who have no precursors - this is a new demographic - in the past it was primarily an old man's disease, and those afflicted were heavy smokers and drinkers. I'm thinking this is not the case with you so....
It doesn't make sense your surgeon wants to wait for you to heal, firstly an area of tissue with cancer present tends not to heal all that well - if at all, and secondly why would he let you heal only to go back in and cut you open again? No only that, in the time that the cells are still in situ they continue to grow, and can potentially seed to the nodes. This is not a sprained ankle or broken leg, time will not help matters it can only get worse - this is cancer.
The primary treatment for non HPV related tongue cancer is surgery, it should all be removed with good margins. Your dr. needs to go back in asap. Some drs make the mistake of thinking "well its gone we're good" only to discover it in the nodes later. This is a tricky disease, by waiting you risk the potential of it spreading, and not only having to have a piece removed from your tongue - but also having a neck dissection and removal of a bunch of nodes. And possibly a need for follow up rads and chemo. All of this because your dr. wanted to wait. No one wants to go back into surgery, I totally get it, but better this than the potential for more aggressive treatment at a later date.
In the past 18 months we've lost three young members to oral cancer, two were tongue and one was gum or cheek, Samantha Kemper 22, Nate Johnson 27 (I think) and MTlisa (26/27 - I believe) - Samantha had 3 recurrences in 18 months. This disease is aggressive, it has a high mortality rate. Another friend who was a few months ahead of me in treatment had a very small one mm superficial cancer, her dr. - obviously very familiar with oral cancer had a feeling despite it being superficial - it was aggressive so he removed lymph nodes as well. Sounds like overkill right? he found cancer in one of her nodes and it had moved outside, she did 33 radiation treatments and 3 chemos even though she was a stage one cancer. 1cm is a stage one, it doesn't sound big, but its big enough. Best of luck... Sorry I didn't want to scare you but you need to know how aggressive this can be. Hugs.