Your esthetic issue could be corrected with Veneers or Bonding but with a less than ideal result. I encourage you to consider Invisalign (about 12 months), Six Month Smiles (about 7 months) or traditional orthodontics (about 2 yrs). You would also need a surgical procedure called a frenectomy - not a big deal. Good luck.
If you are 100% dead set against braces, then you must be OK with a LESS than "perfect" result. While veneers CAN close the space, they likely won't be ideal (in length, width, etc). To minimize this look, you MUST do 10 veneers so the added width is distributed amongst them all. Other options include removing some of the teeth and placing implants to support a bridge, but that will take expert level treatment and not "just any dental office". And of course, your suggested option of dentures, but you will smile even LESS with them and will likely regret that decision.
By far the cheapest, fastest and most conservative choice is braces with a frenectomy.
You do have a very large gap between your teeth. I think it would be in your best interest to consider braces as a first choice. If you were to fix this by doing veneers these teeth would be extremely wide and probably look very strange. I realize braces are a bit of a pain but in the long run you will be much happier with the results. Also consider a laser procedure called a frenectomy to decrease the effects of your labial frenum. Dentures at your age would be a very bad alternative. Good luck to you!
Based on your photos and your objection to braces, I can tell you that a combination of veneers, crowns and bridges could easily fix your teeth in one appointment, but it would cost you several thousand dollars. To most people, several thousand dollars is a lot of money, but if you consider what it would mean to your quality of life, self esteem and confidence, it may be worth it. Drastically changing your smile will likely lead to a drastic change in your life and personal interactions with people. Good luck and I hope this helps. Follow me if you have more questions.
Sarah Thompson, DMD