Make your new label larger than the ones on the drawers and tape it over them. I always take the labels off things I buy. I find the newer the item the easier the label comes off. But it is a combination of the type of glue they used and how long it has had to set. Sometimes the label just won't budge.
I also do this with large padded envelopes I receive and want to save and boxes I receive and don't want my personal information on them when I throw them away. If I pull the label off right after I get it, it comes off with no problem. The longer it's there the harder it is to remove.