All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The time specified for sacrifice is on 10th of Thul-Hijjah (the first day of ‘Eed) in addition to the three days of Tashreeq (11th, 12th and 13th of Thul-Hijjah). So, if the bank which will assume slaughtering the animals will adhere to the above-named times, then you can deputize them to do the slaughtering on your behalf.
"Tahallul" means terminating the state of Ihraam, returning to one's normal state and becoming able to do all actions that were forbidden upon assuming the state Ihraam. There are two phases of Tahallul, the first Tahallul (minor Tahallul) and the final Tahallul. It is not correct to believe that slaughtering is a condition for Tahallul.
As a rule, there are three actions that are essential for Tahallul:
1. Shaving
2. Stoning the pebbles at Jamrat al-'Aqaba
3. Performing Tawaaf Al-Ifaadhah.
The first Tahallul is achieved by doing any two of the above-named three actions, and by doing the third action one would fulfill all that is needed for the final Tahallul.
Allaah Knows best.