How to export hair particle system to fbx format

I have created a mascara brush with hair particles, (File attach). I want to export my brush to fbx file to upload in a website. They need fbx, obj or dae file format. I have done couple of step to export.

Blend File

In the modifiers tab, With the particle system modifier added, i click on convert button, Then i converted to curve, bevel resolution to 0. Again i converted to mesh. For this process my system hang and few time kick me out. But i tried 8-9 times and converted to mesh and exported to fbx. All i got the file size is 1.3 GB. I was shock after going the process a small 2mb blender file converted to 1.3 GB. After going all the process above. When i import the file in Blender i can see the mesh but in render there is nothing.

Is there any other solution or good way to export my file in fbx format with light weight file size. Any suggestion or help. Thanks