It's probably basically fine, to the extent that
Loxodon Smiter and
Panglacial Wurm are also fine. (Panglacial Wurm is a rules headache, to be clear, but it exists.) The fact they're typically used to effect where a card goes is noted but doesn't affect rules practicality. Nobody needs to have priority for the same reason Smiter doesn't need anyone to; you're not activating an ability, you're just exercising an available option.
Bronzeshield Defender just has a replacement effect available from your hand. It gives you the option of replacing "Target creature OneAndOnly controls fights another target creature" with "OneAndOnly puts Bronzeshield Defender onto the battlefield from his hand, and Bronzeshield Defender fights that other target creature." It exists in your hand and functions in your hand; it's available to deploy at a moment's notice.
(I'll note that "that creature fights ~ instead" is ambiguous: which of the two creatures? I'd revise to disambiguate, such as by saying "would fight a creature you don't control" and referring to the creature you don't control. Note that some cards like
Clash of Titans can make your creatures fight among themselves.)
That said, you can get a nearly identical & safer magic-ese effect by using Flash, and it's one that comes with a shields-down moment:
Bronzeshield Defender
1W
Creature - Soldier
Flash
When Bronzeshield Defender enters the battlefield, until end of turn, if a creature you don't control would fight a creature you control, the creature you don't control fights Bronzeshield Defender instead.
1/3
I don't think there's precedent for this ability, but I'd say based on
rule 614.9 for redirection, once Bronzeshield Defender dies the replacement effect can't actually replace anything and fights would occur as normal the same turn.