If you're worried about the Velcro closure, couldn't you pin a thick safety pin through the Velcro to double-secure it? Obviously for a child you'd want a break-away (and even for an adult, a break-away would likely be safer on rides)...but if that's your only objection to a lanyard, I'd think you could fix it.
Or if you brought a needle and thread you could run a few stitches to close the lanyard--the stitches would probably break away if subjected to massive pressure but there would be extra security. Again, you'd be purposely overriding a safety feature, but it's an option for security.
I'd be paranoid of losing my ticket/other things on a lanyard too. But I love the idea of a thin wallet! I think I wore a purse on my last Disney trip (WDW) and before that just used cargo pants pockets.
I can't stand to wear a fanny pack personally, but have no objections to putting a camera/other small bags on a belt. I did buy a water bottle lanyard on my WDW trip but looped it around several times to fasten onto my belt. While I wasn't worried about losing the water bottle

I'm not big on weighty things around my neck.