Sounds like a whole lot of work to me but you are certainly welcome to give it a go on your own to see if you "can". Now I'm not really sure if you may jog around it.....but I highly doubt you'd get thrown in the slammer for trying. I think worst case scenario they would just ask you to leave. Found two links that speak of tracks using the search feature: Stay Fit in Dumaguete ⌛ - Track next to the Pool- and other ???????
Its not the HS's Oval. You can get in and jog around but there is an entrance fee (think entrance is waived for NORSU and NOHS students). The fee is 10p entrance. You can also swim at the nearby pool there as well but again there is an entrance. I can't remember the entrance to be sure but I think it was 40p.
You can jog pretty much anywhere in Dumaguete without having a problem......unless you are carrying around large amounts of cash or backpacks.
Another suggestion is the paved walkway along the water across the boulevard. It is about one kilometer one way. Gets hot after 8:30am.
You can jog around Freedom Park for free. Its beside NORSU on the main highway and while school is out its not busy there.
Yes, that's safe because for d*mn sure criminal types aren't going to be jogging after you. If you are going to be jogging on the roads after traffic dies down, another issue would be dogs. Maybe bring a stick.
What about the use of "Pepper Spray". It has not been outlaw for the evil foreigner types yet. It can usually be found in the barbecue section of the local hardware stores. Has anyone every had an instance in the Philippines where they have used pepper spray?