If you're not timing things now, why are you worrying about timing things for a half? I'd recommend just building up your distance (the coach's favourite is 10% - try not to increase this week's total distance by more than last week plus 10%).
Certainly you'll get a happier all around experience by starting to time yourself - the idea of doing shorter, sharper, harder runs as part of a training programme where you're also doing longer pieces is fairly well understood.
Even if the timing isn't about setting targets - "today's run is going to be 10k at <pace>" - it is about learning about how your body should be reacting to specific pieces of work. Many plans will say things like "60 minutes at 70% of 10k pace" or similar. This is indicative of the effort you should be doing - but if you've no idea what that means, the plan isn't going to be helpful.
It might be useful to consider what is stressful about the plan for you? Do you react badly to targets, to being pushed, to not just getting out there are making it up as you go along, the idea of missing a requested aim?
Why have you decided to do a half? Work back from that to formulate your plan. If it's just to tick it off, time no option, then all you really need to is beef up your distance; so do 33mins next week instead of your normal 30, 36 the week after that - within a few months you'll be well over an hour and well on the way to covering a half!