Firstly, if your only concern about Core is that it is using too much disk space, you can enable pruning. Go to the Bitcoin Core datadir and find or create the bitcoin.conf file (it's just a text file with a .conf extension). Then add the following line to it:

That will reduce the size of the blockchain to ~1-2 GB. What it does is it will just delete the blockchain except for the most recent 288 or so blocks. As you get more blocks, the oldest blocks will be deleted to make space for the new ones.

If you really want to go ahead with transferring the Bitcoin to a new wallet, you will need to do a few things to get abandontransaction to work. First, stop Bitcoin Core. Then go to the Bitcoin Core datadir and delete the file called mempool.dat if it exists. Then start Bitcoin Core with the -walletbroadcast=0 option. Then you should be able to do Abandon Transaction.