I think it is a great idea to have an "alternative" engagement ring but not only for travel, an alternative could be worn to places like an amusement park, concerts, etc 

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"Less than a 1000 dollars"
Lol what? If you are concerned about losing it, why wear your engagement ring in the first place? You can't go 2 to 3 weeks without wearing it?
Or go to a department store and buy a fake cubic zirconia ring.
I wouldn't spend $1K on a faux ring personally. Check out Diamonique jewelry on QVC. You can get faux diamonds in silver or real gold for way less. Some are quite lovely & "real" looking and you won't feel bad about losing them accidentally. And they've got a lifetime warranty, something my jeweler didn't give me on my real diamond.