Changing broker

Um, it likely would, but in the long run, the impact is likely minimal. Say, you sell it all and withdraw it. If it gets processed by tomorrow (not sure if SAXO has any settlement time e.g., T+2), you can probably deposit it in IBKR before tomorrow's trading session opens, and buy as the market opens.

Depending on how well tonight's market looks, at most you'll probably lose no more than 2-5% depending on what your portfolio holds as well.

If you're really concerned, you can use the transfer of positions function instead. This will allow you to transfer your stocks, but at a cost of EUR50 per counter. So, do evaluate if this is cheaper than your expected cost of selling and buying back (including expected market movement). Note that such a transfer might take a few weeks, during which you will be unable to sell your stocks. As such, if any of your positions are short term, do not put them through this transfer process.​​​