I have already looked at many articles on the subject but all of them just say it's possible to find on route 6, or you can breed 'till the cows come home trying to get a shiny. I'm not real big on breeding and was wondering, is there a way to get a shiny honedge that does not involve breeding or the pokemon radar (because it does not work on rout 6 due to the tall grass)?
Yes, any wild pokémon (with the exception of some legendaries) you encounter can be shiny.
However, keep in mind that without any tricks available to increase the shiny rate (Radar, horde battles, etc), your chances are low. Even with the item for 'finishing' the national dex, you are still looking at 1 in 2,000 or so. Also, Honedge aren't the only pokémon in the grass; even if we assume the chance of a Honedge is equal to the other five (It isn't; Bulbapedia lists it as 'rare'), that would take your chances to 1 in 24,000 (assuming a base rate of 1 in 4,000 or so).
Compare this with breeding: You can put an ordinary Honedge in the daycare with another opposite gendered Honedge, 1 in 4,000 (Again, roughly, assuming this is the base rate) chance of each egg being shiny. Take out one of those Honedge and stick in a Ditto (or any pokémon from the Mineral egg group) that was caught in a different region, like Japan, and your chance doubles to 1 in 2,000.
Breeding repeatedly might get a little dull, but if you have to breed "'till the cows come home" to get a shiny, you'll be wading through the grass until the cows came home 6-12 times by comparison.
Im kind of late to this sorry, but the fastest method I found was to use a pokemon with Magnet pull on Route 6. Magnet Pull increases the chance of encountering a steel pokemon to 150% of the usual chance. And as Honedge is the only steel type there, you will encounter more of them. Other pokemon will still show up, but honedge will be the most common, so the chances of it being the shiny you encounter are a bit higher.
Also, if you have some good pokemon with you, I would look on the GTS. There may be some unreasonable offers but if you are persistent, you may be able to get one.