A 3/32" tensioner should work fine with a 1/8" chain
Not if the groove the chain runs in is narrower than the pin length of the chain. There are some ⅛" chains which are only 8mm across (e.g. KMC e101/X101) which are likely to fit, but most of them are over 9mm
Why does it need to be wider? A 3/32" tensioner should work fine with a 1/8" chain.