Taurus, Tungsten has an exceedingly high melting temp and good red strength to boot. I don't think your method would be practical. (it is used in incandesent bulb filaments!) Grinding should not be all that hard to accomplish (a jig may be required to support the wire), they make grinding wheels and specialized tip grinding machines specifically for use with tungsten electrodes for TIG welding as an example. check out your local welding supply store for ideas.
BTW Taurus, Tungsten is a relatively pure metal. Tungsten Carbide is actually mostly nickel or cobalt with Tungsten Carbide particles embedded in it. The actual metallurgy is quite different.