What happens if I am not able to sign the contract myself?

If you are not available to sign the contract, because you are travelling for work or is otherwise predisposed, you can nominate another person to sign the contract on your behalf. You can consider creating a power of attorney document that allows your representative to sign the contract on your behalf. If you choose this option, you should discuss with your conveyancing lawyer to come to an appropriate arrangement, they may also be able to draft for you a general non-enduring power of attorney for your convenience.
However, it is very important when creating such an instrument that you nominate the appropriate person to exercise your right. Once the contract is signed by your duly appointed attorney, it will be as if you have signed the contract yourself and you will generally not be able to back out of it.
It is always recommended that you reserve the task of signing the contract to yourself and the power of attorney should only be used as a last resort. This is particularly true in context of the modern age where contracts can often be signed on the go with technologies that allow for e-signing.