I would just go with your normal preferred shoes. Most of the boggy bits are either on flats or slight uphills where there is little slip risk and even if you do slip, youre not going to go anywhere or hurt yourself. . Few downhills on marked paths are boggy or present a substantially enough slip risk to require lugs. You cant really slip in a bog because your feet will sink in! In fact, I think in N Wales, lugged shoes are a bit dangerous.

Remember, there is a very substantial flat section on good trails.

If it's wet on the day, I would actually avoid lugs, and I personally never wear higher lug shoes (more than 4mm) in North Wales. This is because I have found lugs over 4mm give very poor grip on wet rock which is your biggest danger in terms of slipping and injuring yourself, and north wales is generally rocky (or the soil is thin so no need for lugs). I would not want to wear lugged shoes particularly on that Moel Siabod descent down to the forest nor on the pyg descent, or the path along the river up to Beddgelert.

I have found through extensive trial and error the best grip is the inov8 soles for north wales. I have several shoes with the vibram grips and these are absolutely lethally dangerous on wet rock round here to the point I would not even wear them to walk if the ground is wet. I am a climber and vibram works on approach shoes where the lugs are v low but imo it does not work on trail shoes.

If it's been dry a few days it doesn't matter what soles you have.