In that case, you don't have any choice but to rely on a third-party.

Firstly, a timelocked transaction isn't something that can be broadcasted now, then executed later. It'll be rejected by nodes if the locktime hasn't passed yet.
Its use-case is: it has to be given to the beneficiary or a third-party that will broadcast it at the specified time/block height.

Secondly, a timelocked output script like the examples will not be spent automatically, it has to be spent by the beneficiary himself or a third-party to send the bitcoins to the beneficiary's wallet.

Lastly, given that it has to be kept secret to the beneficiary, the third-party has to keep the necessary information to broadcast or spend your bitcoins instead.