But can it be done without causing any problems with other computers in the network? And do you know any good open ports?
Yes. The ports that you SHOULDN'T use would be commonly-used ports, namely 80. I would recommend a higher up port, you stop using common ports when you hit about 10000. I personally use the default for Blockland, but I would use a port in the 4000s range if I had to change it, probably.