I have heard of an engagement bicycle.
I am totally traditional and love my wedding ring and the symbolism of it (itis a plain gold band) actually more than my engagement ring or any other jewelry (and I am real jewelry gal) but hey, you are not me and that's fine. It is convenient in a society to have some sort of marker as to who is married (and off-bounds) and who is not married and thus available, whether it is a ring or a red dot on the forehead or whether is that unmarried girls have loose hair and married women tied up hair--but that's not a reason you HAVE to do whatever, if it makes you miserable. I have unfortunately been hit on by men too many times (when wearing an obvious wedding ring) to think that wedding jewelry is actually a real protection in any way. So, so long as you are taking your vows and you and your future husband know that you are going to be faithful to each other regardless, forget about the ring(s).
Since you are on this forum, maybe you would like an engagement handbag?
best of luck to you in any case and congrats!