You might be able to, but it's really not worth the effort.
ETA: Are Will the parent shares physical certificates as well, or do will they reside at a brokerage firm? If physical, you will get physical certificates (because they won't have any other way to give them to you); if not, you will have to ask for physical.
Physical certificates work sort of like the title to a car...you can't just pass them around or do anything with them w/o going through the (equivalent of the DMV) transfer company that the parent company (typically) hires to handle administration of stock dividend and ownership details for them. If you want to sell, gift or even send them to a brokerage firm you will have to file paperwork, and it's not real simple paperwork: it requires what is known in stock market parlance as a Medallion Signature Guarantee...sort of like a notary but harder to find (you'll have to go to a bank that has one).
IMO a) you are introducing another variable into the equation which makes it even more likely for something to go wrong (which it seems you are worried about), b) spinoffs occur all the time* and there is no hocus pocus and the new stock doesn't get lost in the ether and c) it is a big hassle to do anything with them (other than put them in a safe deposit box and forget about them...until they become a hassle for you or someone else).
Additionally, unless there is something unusual about your transaction and/or you own a ton of the parent stock, you won't end up with much of the spinoff...so it's a lot of effort for not much, at least initially. Unless you have very low or zero commissions it may not be worth it to sell them again, at least not right away.
Last year I think I had 3 companies spinoff part of their operations...went straight into my account on the effective date. If I had wanted to sell them immediately I could have done so.