Walking is most common on 5k events where people are just getting started or overcoming something... like a physical limitation.
I’d think the intuitive order of ‘things to accomplish’ would be to finish running a 5k before walking a 10k. Having said that, there is no wrong answer and you’re way ahead of anyone on the couch. You most certainly won’t be alone in walking and I’d guarantee no one will judge you.
I will present the opposite situation for your consideration though. April is a long time away. If you keep up the training, you may find the 10k too short and wish you entered the half-marathon
I’m not a runner and only did a 5km in December 2018. By April 2019, I had finished the Disney Star Wars half-marathon. You’re way ahead of me if you’re training already. Aim high and don’t doubt you can do it.