Perhaps employing iodine in the place of mercury may work.
Some background on the proposed chemistry starting with Wikipedia on Iodic acid, to quote:
Iodic acid, HIO3. It is a white water-soluble solid...Iodic acid can be produced by oxidizing iodine I2 with strong oxidizers such as...or hydrogen peroxide H2O2,[1]...When heated, samples dehydrate to give iodine pentoxide. On further heating, the iodine pentoxide further decomposes, giving a mix of iodine, oxygen and lower oxides of iodine.
Now, the action of $\ce{I2}$ on water slowly forms $\ce{HI}$, $\ce{HOI}$ and $\ce{HIO3}$:
$\ce{I2 (s) + H2O (l) -> HI (aq) + HOI (aq) }$
$\ce{3 HOI (aq) -> 2 HI (aq) + HIO3 (aq) }$
However, apparently more rapidly, per Wikipedia on Iodine to quote:
Iodic acid is most easily made by oxidation of an aqueous iodine suspension by electrolysis or fuming nitric acid.
So to summarize the proposed chemistry per above, the presence of oxygen from the electrolysis of water acting on a suspension of iodine forms, in part, Iodic acid. The created $\ce{HIO3}$ can be isolated or converted into iodate followed by its thermal decomposed to liberate oxygen, iodine and iodine oxide in a partial recycling.
For those interested in the particulars of the underlying chemistry, one possible explanation is the presence of electricity (a source of solvated electrons) and oxygen could result in the formation of the superoxide radical anion per the reactions:
$\ce{e- + nH2O -> e- (aq)}$
$\ce{O2 (d) + e- (aq) -> .O2- (aq) }$
A fast reaction of the superoxide with the $\ce{HOI}$ intermediate may result in Singlet oxygen (and the hydroxyl radical). This is speculated from the reported reaction of hypochlorous acid with superoxide, namely:
$\ce{ .O2- + HOCl -> ^1O_2 + .OH + Cl- }$
Singlet oxygen directly or indirectly, via its known reaction with water forming $\ce{H2O2}$ (which was also noted above to act on an iodine suspension), could explain the conversion of an aqueous suspension of iodine to $\ce{HIO3}$.
Note: If my depiction of the chemistry is correct, no need for an external electric source to introduce the needed solvated electrons. Just construct an electrochemical cell (similar to the so-called Bleach Battery) composed here of an aqueous iodine suspension with an Aluminum anode and say a copper cathode. Pass air into the cell to convert the iodine suspension to iodate, thereby capturing the oxygen for future use.
Caution: if Aluminum Iodate Hexahydrate (referred to as AIH) is possibly created in this electrochemical cell synthesis, it is considered a strong oxidizer (even as a hydrate), so mixed with the wrong compounds (say carbon from employing a graphite cathode) and heated may display notably energetics.
[EDIT] Interesting related article: High power rechargeable magnesium/iodine battery chemistry.
Also, a related galvanic cell synthesis, albeit, with advanced electrode design in this work: Energy-saving synthesis of potassium iodate via electrolysis of potassium iodine and O2 in a membraneless cell.