Vinegar/Water Stuff-Up... tips for cleaning?

Hi all,

Apologies if wrong section but purchased a (possible) mid-century chest of drawers, the faces made up of veneer. Was originally planning to restore but due to no backyard or great ventilation, have decided to just give a good clean as much as I can without disturbing the original finish.

Had a google and came across equal parts vinegar/water being a wise option to get rid of gunk before wiping off with a damp cloth then dry. Seems to have left a white film over the chest of drawers that doesn't look particularly disastrous but wanted to check here if anyone knew the best, non-invasive form of cleaner that may get rid of it?

Cheers!

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