Since I and two rabbanim I asked didn't find classical sources addressing this case, I think we have to break down your question into three
Are you forbidden from opening the ark?
Do you have to open the ark?
Should you open the ark?
You are clearly not forbidden from opening the ark. A yachid that wants to pray in a shul in front of an open ark can do so. The gabbai will open it to prepare the sifrei Torah and a bar mitsva will open it with his teacher when learning to chant the parasha.
On the other side, we do not find a halacha that you have to open the ark. It is a custom amongst Ashkenazim, see e.g., here (citing Mateh Efraim 619/46 and Otzar Minhagei Chabad 199 in name of Sefer Haminhagim) but Sefaradim don't do so.
The more difficult question is whether you should have done so? On one side, the whole point of opening the ark is to inspire the kahal which also works without a minyan. On the other, Hazal prescribed a certain form to the tfila b'tzibur which we are not deviating from. For instance, you don't read the Torah publicly if there is no minyan even if you theoretically could (possibly without blessings).
It is more a question of "halachic sensitivity". The two rabbanim I asked said that, since it was a custom when praying in minyan, one shouldn't do so when praying without. One suggested that, if the majority of the tzibur wanted it, there is nothing to prevent it, but it shouldn't be the default option.
Since other rabbanim might rule differently, as always, CYLOR.