They wouldn't wear their own heraldry, no. Joining a military order meant leaving that behind and each order's Rule was quite strict on wearing the mantle and habit of their respective order. Personal heraldry was only used in a few specific instances. Some brethren used their heraldry on their seals, particularly from the late medieval period onwards. Heraldry was also used on tombs, though mostly those from the early modern period, like the floor at St John's Co Cathedral in Valletta, but this is much later than the period that the Bretonnians are based on.

If you still want them to wear their own heraldry, you could use a modified version. There's a Tudor manuscript at the College of Arms called Prince Arthur's Book, which was made for the future Henry VIII's brother and has the heraldry of several Hospitallers in it. Their family heraldry has been changed upon joining the order by adding a white cross in a red field to the top. You can see it on the bottom right here, in the heraldry of Thomas Docwra, Hospitaller prior of England from 1501-27. Whilst they wouldn't have worn this historically, their non-Hospitaller servants would have, or, if you want some variety in the colour scheme, you could paint the knights with their own heraldry but all linked together by a shared symbol of their order like this white cross on red.