I'll be honest, I wasn't even aware dress shirts were sold at Walmart. Just my thinking on this is you're about average, and your comment seems to back that up. I don't think of J. Crew and Brooks Brothers as particularly "elite," but that might just be me.
I don't argue that there isn't a big market below the $69 price point, but as jsmthroway is saying, there's a large market at our price point, and up to now, it's almost exclusively off-the-rack. We think we can provide a high quality custom product where previously the only option at that price was off-the-rack.
There is a large market. How are you planning to reach it?
If you cannot go lower, I'd consider a partnership with an existing brand. You'll have to have an insane marketing budget to compete with existing clothing brands without viral.
If you can partner with Brooks Brothers (established in 1818, and part of American preppy folklore), J. Crew, Men's Warehouse, or similar, you'll have an easy time breaking in, although a much harder time getting most of the profit share.
Unless you're planning to raise very substantial amounts of money, advertising might not be the most effective tactic. It's worth perhaps playing with, but not doing more until you've seen it work. You're a small business. You've got a highly unsegmented market. In unsegmented markets, advertising is mostly about brand building. That works well if you're Coca-Cola, but much less well for small start-ups.
Word-of-mouth can work well, but you've got to understand your customers, the networks, and the levers you can tweak to change rate-of-growth. I was suggesting price/quality/margin as one of those levers -- you want to be appealing to as many customers within your customers' networks -- but there may be others if that one is unappealing.
Compare the market caps of Walmart, J. Crew (which was recently purchased), Brooks Brothers (from a sane P/E ratio), Armani. Heck, try a TJ Max or similar (to avoid companies with major non-clothing businesses -- which, coincidentally, J. Crew does have).
There's everything from $13 ones at Walmart to $70 - $90 ones at J. Crew and Brooks Brothers (MTailor price point) to $300 Armani shirts (and above).
Having spent a lot of time in in-person custom shirt shops, our $69 shirts are comparable in quality to shirts you would buy there for $125 and above.