Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother, thank you for your question and for your interest in Islam’s teaching concerning wedding.
Walimah is optional (Sunnah) for the wedding. So, it can be done in the way the two families decide. Also, they can skip it if they cannot afford it.
Responding to your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, stated:
For the ceremonies of nikah (wedding) and its walimah (wedding food), it is permissible to make them anyway agreed upon by the two persons and their families as long as they do not do anything not permissible during them such as mixing men and women without appropriate clothing for all or serving alcohol, etc.
It is also permissible to cancel the ceremony and make a small private meeting with only two witnesses. The walimah is a Sunnah but it is not prohibited to cancel it as well.
Allah Almighty knows best.