"Spouse" is a gender-neutral word that implies "husband or wife" (you wouldn't say "your spouse" unless you considered yourself married to the referent). "Partner" doesn't imply either legal or self-identified marriage to me, though it does imply commitment. (As others pointed out, "partner" can also mean a non-romantic business or professional partner, which can be confusing.)

But more to the point, why *can't* you be discreet about marriage? It's true that we usually aren't, but that just begs the question. If I've been with my (imaginary) boyfriend for 40 (imaginary) years but don't want to refer to him with terms usually associated with marriage or monogamous partnership, either because I'm not monogamous and don't want to imply I am or because I simply don't like the connotations, why is it more wrong for me to mention him in a work context as "my boyfriend" than it would be if we happened to call each other our "husbands" instead?