Do you think it's a better idea to move them to a lightning wallet like on electrum for example before the transaction fees get too high? I want to avoid paying a big amount just for one transaction in the main network
The fees are already too high. The best time to open a lightning channel is when fees are low because it requires an on-chain transaction. Lightning is meant for smaller payments so perhaps you shouldn't move your entire cold storage to lightning. I would just open a channel big enough for a few payments and occasionally top it off.