"I warned everyone beforehand that death IS a possibility in my games"
Then you lied. Sorry, that might sound a bit harsh. What I mean is that you warned them that death is a realistic possibility, but you have planned for scenario where death is guaranteed, or at the very least, is the cost of doing business with you - one of you must die to keep the game moving forward. "You might die" and "I am going to kill at least one of your characters" set up entirely different game expectations. The former tells me to expect challenging, high stakes encounters that I can overcome with some ingenuity and luck, but "I'm going to kill one of your characters" tells me to expect you to present an insurmountable challenge. You said "you might die", but what you meant was "you are going to die".
I wanted to do a little something that would remind them that death can happen
This is just not the way to do it. For two reasons - the first outlined above. The players are expecting challenges, and you intend to present them with an impossible dilemma, which, in the moment, is likely going to be poorly received.
Your plan will probably send the opposite message.
The second reason: you say you want to do something to remind them that death can happen, but artificially forcing death upon them only to reverse it by saying "Surprise!" takes away from the stakes you are trying to present. Your plan does not say "the stakes are high, the challenge is real", it says "the stakes are low, the challenge is fake".
Keep the stakes high, and deliver on your promise.
Instead of killing a character just to Deus Ex Machina them back to life, make the puzzle solution costly. I've done something similar in a dungeon crawl, but I didn't kill them, I just increased the challenge. The party was met with a door and a riddle, with a similar solution - blood. Once they figured out the narrative solution to the puzzle, blood, I explained to them the mechanics. They had to sacrifice hit dice to unlock the door. The party of four 8th level characters had 32 hit dice between them, and the door required 16 hit dice sacrificed. The important part of this solution is that the party could strategically decide who would give more and less hit dice. There was a price to pay, but they had control over how that price was split between the party members. They opted to let the barbarian with the most valuable (d12) hit dice keep all of them, with the expectation that the barbarian would be taking the most damage as the frontline tank moving forward. The party felt like they still had control over their destiny, despite having to pay a price to advance, and the price increased the risk of death moving forward, but it did not guarantee death. In your situation, they are going to go into it feeling like they have little control: "one of you has to quit playing or we all quit playing".
I'll leave you with this guidance from the intro to the Dungeon Master's Guide:
You’re the DM, and you are in charge of the game. That said, your goal isn’t to slaughter the adventurers but to create a campaign world that revolves around their actions and decisions, and to keep your players coming back for more! If you’re lucky, the events of your campaign will echo in the memories of your players long after the final game session is concluded.
The success of a D&D game hinges on your ability to entertain the other players at the game table. Whereas their role is to create characters (the protagonists of the campaign), breathe life into them, and help steer the campaign through their characters’ actions, your role is to keep the players (and yourself) interested and immersed in the world you’ve created, and to let their characters do awesome things.
Knowing what your players enjoy most about the D&D game helps you create and run adventures that they will enjoy and remember. Once you know which of the following activities each player in your group enjoys the most, you can tailor adventures that satisfy your players’ preferences as much as possible, thus keeping them engaged.
This encounter as you describe it does not "revolve around their actions and decisions", it revolves entirely around you forcing your preplanned outcome, an outcome that at first looks exactly like slaughtering adventurers.