Security is a very broad topic and nothing is totally safe.
Physically being in a public place adds all kinds of risks, obviously, like a camera capturing you typing a pass phrase or someone stealing your device.
For the technical part of your question, in simple terms, using a wifi on a public place will increase any existing vulnerabilities on your system, or in the way you operate with it, and to a lesser extent also expose some new vulnerabilities which would be hidden if you connected from your home.
So, to asses the risk it is very important to evaluate the specific system are you using: your device, operative system, wallet software and also whether your trading site uses 2-step verification.
Important advice is to reduce the risks by installing only the software you need, or as alternative properly configure a firewall.
Most importantly, your internet browser should be pristine clean without any adds-on installed.
Under this conditions, every time you connect to your trading site, just make sure to enter the URL correctly without any typos. The URL will always start with 'https://' and you should see the green lock icon your browser displays on the left to the URL. This lock icon tells you your browser connection is encrypted and also shows the certificate it uses to make sure you are connecting to the real trading site and not some fake.
With this simple precautions you should be fine: a hacker can never steal your credentials from an https connection assuming your device is totally free of malware. A VPN connection, or your home connection, will not make any difference in this regard.
Your wallet software, if any, should also encrypt any sensitive traffic.
You can ask the network security staff to use a WIFI access point supporting upgrades to the firmware, and staying up-to-date with any patches the manufacturer provides.
This provides an additional layer of security against other people near you by providing an encrypted connection between your device and the wifi hotspot so the people around can not spy on your traffic out of the thin air.
Without wifi encryption, even if the https connection itself is secure, people could still figure out which sites are you connecting to, for example, but they are not able to see the details of your operations or passwords you type, because it is all encrypted by the https connection. The network administrator or internet provider company could still know what sites you connect to, though.
Even then, remember bugs are everywhere, and a hacker will allays have a greater chance of breaking into your device if he is near you.