how would i go about throwing an NON-CONTACT martial arts tournament?

A license?

You've got a lot more to think about. I would strongly suggest you contact someone who has done it before. Off the top of my head, you must consider these things:

insurance

permits

competitor waivers

parental consent

venue deposits

advertisement

judging and/or refereeing

equipment (mats, ropes for sections, tables, chairs, garbage cans, etc)

first aid (fire department may stipulate equipment and training required)

parking (municipality may have minimum parking space requirements)

police (municipality may require for sport events)

cleanup

trophy/prizes

AV equipment (microphone, amplifier, recording)

signage (labelling for sections, billboards, announcements)

interior traffic control (walkways, cordons, etc that the fire department will require)

occupancy enforcement

taxes (on income)

vendors (equipment, food)

sponsors

department of health issues (for food-related issues)

logistics:

-acquiring a venue

-deciding on dates

-conflicts with holidays or other events

-contingency dates

-communicating with coaches, competitors

-bathroom facilities

-layout of competition venue

-eating locations

-spectator seating

-competitor ready areas

-competitor practice and waiting areas

rules:

-dispute resolution

-judging guidelines

-point awardng

-determination of winner

-tie conditions

-breaking mediums

-who will supply boards

-age/weight/experience categorization

-late arrivals

If it's open tournament, you need to consider how you will judge styles with which you have no experience. For instance, say you have a staff of referees and judges that is experienced only in taekwondo. But you have a team that is competing in Karate forms. How will the TKD judges fairly judge the Karate kata?

You should acquire volunteers to help, then divide the above issues into logical jobs, then groups the volunteers into teams. Volunteers can be part of multiple teams, and teams can execute their tasks at different times depending on need. Each team should go away and privately plan on how they will execute their assigned task.

Before anything is done, each team should have a kickoff meeting where there is a Q&A that ensures everyone knows what they're doing, and if there are any inter-team dependencies, that should be established. Also, any unanswered questions should be addressed and dealt with appropriately. As in carpentry: measure twice, cut once. Therefore, plan properly, execute once. It's much less expensive to make mistakes this way.

Good luck.

You will need to obtain insurance.

If you really know what you're doing, you'll be able to get it.

If you can't get it, then think again about whether you are prepared to do something like this.

Do you have broad experience organizing, promoting, and running tournaments, conferences, or other similar events? Do you know how to size and organize your budget and manpower (both paid and volunteer)? Do you know what the timeline for promotion, bookings of facilities and equipment (everything from chairs and tables, to mats, to AV equipment), etc. should be?

The way you phrase your question gives the impression that it's somewhat of a pipe dream--not an actual plan. Be sure you have thought it out well before you get started.

Non-combat? Guess what, you are going to have an influx of crappy mcdojos, and almost no legit schools, and the legit schools that do show up are going to be mainly beginners.