Welcome, Maine!
My bottle supplier (http://www.specialtybottle.com/glassbottles-2.aspx?gclid=CN2Q9pCz1asCFSkbQgodkCHROg) sends unlined caps with bottles that have reducers. The caps still don't fit down as far as a plain bottle with lined cap, but I've found the unlined caps with reducers seal up just fine as long as proper processing procedures are followed.
just a side note- make sure your sauce actually needs a reducer. Many times I've opened bottles and can't get the sauce out through the reducer, so...off it goes. No need to make more work and more $ if it's not needed.