The synthesis and biological evaluation of potent hydroxamate-based dual HDAC1/6 inhibitors with modest HDAC6 preference and a novel alkoxyurea connecting unit linker region are described. The biological studies included the evaluation of antiproliferative effects and HDAC inhibitory activity in the human ovarian cancer cell line A2780, the human squamous carcinoma cell line Cal27, and their cisplatin resistant sublines A2780CisR and Cal27CisR. The three most potent compounds 1g-i showed IC50 values in the low μM and sub-μM range. 1g-i revealed low nM IC50 values for HDAC6 with up to 15-fold preference over HDAC1, >3500-fold selectivity over HDAC4, and >100-fold selectivity over HDAC8. Furthermore, their ability to enhance cisplatin sensitivity was analyzed in Cal27 and Cal27CisR cells. Notably, a 48 h preincubation of 1g-i significantly enhanced the antiproliferative effects of cisplatin in Cal27 and Cal27CisR. 1g-i interacted synergistically with cisplatin. These effects were more pronounced for the cisplatin resistant subline Cal27CisR.