First of all, your wife need not worry that it would be a mortal sin to wear the dress. Mortal sin requires grave matter; so, unless the dress exposes so much skin that a woman could be arrested for wearing it in public, it seems safe to say that wearing this dress does not rise to grave matter. In any case, if there is fault to be assigned here, it would be the bride who chose these dresses without input from the women she asked to wear them and apparently without consideration for whether the dress would be appropriate for an amply-endowed woman.
Secondly, your wife does not need the bride’s permission to wear a shawl over her shoulders for the church ceremony. The bride may choose the dress she would like her attendants to wear – although it is considerate for a bride to seek input on the dress from the women expected to pay for the dress – but being a bride does not give her license to dictate the attendants’ appearances down to the last accessory. Believing that one can force an attendant to attend a sacred religious ceremony in an outfit the attendant fears will make her appear immodest is hardly an attitude appropriate for a Catholic entering the sacrament of matrimony.
I recommend that your wife approach the bride projecting an attitude of confidence that the bride will accommodate your wife’s legitimate concern. Your wife might offer to wear the shawl only for the ceremony and to remove it for pictures and the reception. I find it hard to believe that someone who considers your wife a close enough friend to ask her to be a part of her wedding would refuse such a compromise. But, if she does, your wife might simply state, “Then perhaps it would be best if I simply attended the wedding as a guest.” The bride then has the choice to accommodate your wife or to allow her to drop out of the wedding party.