Network datasets can be viewed in ArcMap even if a Network Analyst license isn't installed. So your colleagues could simply add the network dataset as a layer to view the arrows.
However, it does take longer to draw network datasets in ArcMap than feature classes with the same shapes. This is because network datasets don't actually store geometries--they continually look them up from source feature classes instead. Therefore, you probably would want to use the source feature classes to render directionality. Here's how:
1. Add the source feature class to ArcMap. I'll assume it's called Streets.
2. In the Table of Contents, double-click Streets to open the Layer Properties dialog box.
3. Under the Symbology tab, click Categories > Unique values.
4. Click the Value Field drop-down list and choose the field that stores directionality. I'll assume the field is called Oneway and has the following values: FT for one-way streets in the from-to direction, TF for to-from, N for streets that don't allow travel in either direction, and <blank> for streets that allow travel in both directions.
5. Click Add All Values to add FT, TF, N, and <blank>.
6. Set symbols for each value. For FT, I would choose Arrow Right Middle (or Arrow at End); for TF, Arrow Left Middle (or Arrow at Start); for N, a red line; for <blank>, a gray line.
You can save the Streets symbology as a layer file and share it with your colleagues.