I've had this done.
All the cutting of 'V's etc made no difference. I was attending a chiropodist every couple of months for about 20 years and paying about £30 each time, for really not much benefit. The consensus was that I needed the outer side section of each big toenail removed. Approx £650 for both toes. And I was afraid.
Removing only part of the nail means I can still have polished toe nails 
Eventually it had to be done. I went to my GP and he referred me to the NHS Podiatry Clinic. The wait wasn't awfully long, about two months for an assessment. Then about another month to have the surgery done. Best thing ever.
The sliver is cut from the outer sore side of the nail and then that section of the nail bed is treated to stop it growing again. This was about 4 years ago. One of mine tries to regrow from the nail bed but I just keep it trimmed back. Bought really good clippers and pincer cutting thingy, very sharp and accurate.
The toe is frozen to have the surgery and a turnoquet is used to stop any bleeding. When the numbness wears off it's all a bit tender but nothing unbearable and there is a bit of bleeding. Used paracetamol for a couple of days. Dressings need changed and checked a time or two to ensure that healing was progressing as it should.
The dressing is only bulky for a few days, then it's minimal dressings. You'd be able to wear trainers OK. Maybe sandals for the first couple of days. It's not long until you'd be into ordinary shoes even if healing wasn't fully completed.
And now.... the bliss of wearing any shoes without fear of toe nail pain is great, I'd recommend anyone to go ahead.
If you can get it done via the NHS go for it.
Depends on the waiting list and how painful your toe is whether you'd want to pay or wait on NHS.
I'd do it again is a heartbeat.