IMHBAO, Jacobite shirts are costume pieces and look silly in church or anywhere where modern dress is the norm. A vest or waistcoat would be alright and it should be relatively easy to find one. Much easier an cheaper than a kilt jacket. But really, if you just wore a shirt and tie, that should be sufficient. I always wear my bonnet when I'm playing, even in church, even when I'm not playing, if I'm still in the role as piper, i.e. waiting between sets. When my part is finished, though, I would remove the hat.

What's the event? If it's somehow vaugely Scottish in nature, like a Kirkin' O' the Tartan or something, then you should dress the part. But if you're just playing for the music, you really could just skip the kilt and all the paraphenalia. It is possible to play the instrument without dressing different from everybody else.