I would try this. Recreate the conditions. If you have enough seam allowance try and remove a similar piece of tape and dab with soapy (mild soap flakes) water. The backing may come away and may take some of the sticky residue with it.
My concern is the the age of the velvet and colour fastness. The colour is likely to come out. It depends where the tape is located if any colour damage can be touched up.
I'd also call up a museum that has a costume collection and see what they would advise.
Check this link for some 1930's tips:
http://vintagesewing.info/1930s/31-ldc/ldc-14.html
Here is the cleaning tip for silk velvet;
"Cleaning Silk Velvet.—In order that silk velvet may be cleaned easily and quickly, it must be flat and smooth; therefore, lay the piece on the top of an ironing board, stretch it so as to remove all wrinkles, and pin it on all four edges to the cloth covering of the ironing board.
The actual cleaning is done generally with chloroform applied by means of a small sponge. Pour a few drops of chloroform on the sponge and rub it carefully over the pile of the velvet. The chloroform will evaporate very rapidly, so, as soon as the sponge becomes dry, pour on a few more drops and proceed as before. In addition to removing stains and spots, this method of cleaning will restore the color of the velvet to a certain extent. In using chloroform, remember to do the work out of doors, on a porch, or near an open window, never in a closed room.
Wood alcohol or one of the other spotting agents may be used instead of chloroform with good results, alcohol being the best, for dark colors.
Whatever solvent you use, do not consider the velvet cleaned until you have steamed it. This process, together with the gentle brushing you give the velvet during the steaming, will raise the nap."