If it has to be ambidextrous, you are restricted (?) to guns like the Ruger #1, Browning B78, Winchester 1885, Stevens Favorite, CPA 44-1/2, Sharps, Encore, Browning BPS shotgun, Baikal single shots, over/unders or double barrels, Merkels, H&H's, Westley-Richards,Jeffery's.
Unfortunately, with bolt actions and semiautos and other than a few pumps, you would have to buy a LH and a RH version, if they are avail in both.
Biggest restriction will be your pocketbook.