Honestly, it's not great, and I sat that as a mum if 2 under 2 that are now a bit bigger. My youngest is about your eldest's age and I can't imagine going out without letting her out to walk at that stage. And we've for a garden to play in. If this is the only outside simulation your toddler gets, then they need that exercise probably as much as you do, possibly even more, even if they can't communicate it yet.
But all means push your toddler, but do it to a park where they can run around and burn off energy.
If it wrecks the nap, then so be it. At 3m there will be other naps that day. I personally find a single buggy plus sling combination better than a single buggy, and there's less chance of them waking eachother that way. But yeah, if baby wakes you'll have an awake baby and a toddler, but that's kind of the deal with a small age gap. And I know that sounds harsh because you're struggling, but that's why we've got slings, and two arms. The multi tasking is crazy, but it's part of it. Learning how to manage a busy toddler out and about with a baby is something you are going to have to learn, either now when your youngest is relatively mobile, and will have multiple naps a day, or when they are older and the stakes are higher. Normally your second is basically thrown into life - ie my second was in a sling at soft play within a week, and was left half dressed on the floor of a playground the following week when mid nappy change my eldest ran out of the park towards the stream. It's brutal, it's downright ridiculous at times, but it's so worth it. Eventually they'll start playing together and hugging and being really good company for eachother, and that feels wonderful. It's still hard (in some ways easier than when they were yours age, in others harder, but v different)
When does your eldest nap? If you can align a nap then that is amazing as it's the nearest you'll get to a proper break.
Ps, learning to feed in a sling was life-changing for me. It meant my little one basically lived in slings for the first few months and means you can still chase your toddler round the park, push them on swings, get their lunch etc, without even stopping to feed.