Apex Treasury Corp II

Exhibit 4.4 WARRANT AGREEMENT THIS WARRANT AGREEMENT (this “Agreement”) is made as of [●], 2026 between Apex Treasury Corp II, a Cayman Islands exempted company (the “Company”), and Efficiency, Inc., a Delaware corporation, as warrant agent (in such capacity, the “Warrant Agent”, and also referred to herein as the “Transfer Agent”). WHEREAS, the Company is engaged in an initial public offering (the “Offering”) of units of the Company’s equity securities (the “Units”), each Unit comprised of o…

S-1 · 2026-10-13 · 0001213900-26-108751

Exhibit 99.1 Consent to be Named as a Director Nominee In connection with the filing by Apex Treasury Corp II (the “Company”) of the Registration Statement on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), I hereby consent, pursuant to Rule 438 of the Securities Act, to being named as a nominee to the board of directors of the Company in the Registration Statement and any and all amendment…

S-1 · 2026-10-13 · 0001213900-26-108751

Exhibit 99.2 Consent to be Named as a Director Nominee In connection with the filing by Apex Treasury Corp II (the “Company”) of the Registration Statement on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), I hereby consent, pursuant to Rule 438 of the Securities Act, to being named as a nominee to the board of directors of the Company in the Registration Statement and any and all amendment…

S-1 · 2026-10-13 · 0001213900-26-108751