The ONLY thing I'd advise against is doing something that would ruin
his proposition in some way - if his idea of romantic is bringing it in your glass of champagne (GenSpec, please don't do this, and if you read this, NAUGHTY!), don't put yours in his because it'll make his less "important".
That aside, the monetary value of a wedding ring or engagement ring should be quite unimportant. Your ring to him is (possibly/probably/perhaps/...) more "personal" than his to you (in the sense that you picked yours out so it isn't a surprise or whatever; they're hopefully both a show of enduring love and eternal companionship and such
), why would it be "silly" or lessen the moment?
I know it's not *quite* the same, but still: when my grandparents got engaged, my grandfather gave my grandmother a worthless nickle (or brass, I confuse my metals in English) ring, of the kind put on the "pin" in a hand grenade. Why? WWII - my grandfather couldn't very well afford an actual valuable ring, just returning from working in Dresden and all that. Later, my grandfather replaced that ring with one more "valuable" - but my grandmother always stayed much more attached to that one, because it was from the heart, not the wallet.
Of course you have to decide for yourself - I assume you know soon-to-be Mr Dill better than us. But "silliness" or "lessening" anything shouldn't figure into it at all.
Don't give yours
before his if you've already agreed he's going to propose (because that might "lessen" the "special" of the moment when he proposes to you - and while I'm all in favour of the woman proposing, you said he could do it
); whether you give it at the same time or later, choose yourself. As has been said above, doing them separately will allow you an extra day to splurge/remember fondly.