WGS84 is a coordinate system, but it's a Geographic coordinate system, which means it's referenced to a sphere (or ellipsoid). Note that it's also a datum, so if the full name you see under the coordinate system properties is WGS84, that's GCS, but you may also see WGS84 as part of a coordinate system name. You want a Projected coordinate system, which is where that sphere is flattened out. UTM is one such system of projections. Based on the park name, looking at the map jonathanw linked to, and a quick search on 'park name utm zone', it looks like UTM Zone 36 South would work for you.
ArcGIS is capable of reprojecting on-the-fly, but if you want to use the data in other software and even for some tools in ArcGIS it's best to make sure everything is actually in the projection you want. That's what the Project tool is for. It takes an input file and reprojects it to a new output file using a different coordinate system you specify. You can find it by browsing through the toolboxes in the Catalog window or just typing Project into the Search window. Note that you want the Project tool, not the Define Projection tool - that's for when the projection isn't set correctly; it doesn't change any coordinate values.
If the datums are different between the two coordinate systems you use, you have to apply a transformation. There will usually be a warning about this. But if you use the same datum, you don't have to worry about a transformation. So you'll launch the Project tool, select your first file in the top box, type in the name of the output file or feature class in the third box (maybe you just tack UTM36S onto the end of the original filename to keep which is which straight, and make sure it stores it in the right path location - you may need to browse to where you want it with the button to the right), then click the button next to the Output Coordinate System box. In the resulting dialog you'll want to expand the
Projected Coordinate Systems folder and drill down to
UTM > WGS 1984 > Southern Hemisphere > WGS 1984 UTM Zone 36S. Since that's the same datum as your original data, you don't have to worry about the transformation box. Click Ok, and then repeat for all your other files.