If you have access to the private key, you could import it into a wallet that has the Bitcoin blockchain already indexed. An example of one would be electrum.
https://electrum.org/#home
Topic: Want to transfer my wallet to my laptop. (Read 268 times)
Basically I bought 5$ ( 0.01774393 BTC ) worth of bitcoin before 2 years and now they are worth 73$ but here is the problem but since they are on my Bitcoin Core on my old PC it is downloading exteremely slowly ( Currently at 2 years 26 weeks left ) and a total of 33,7 GB.... I've got a pretty good laptop and good internet speed. Is there anyway I can transfer my wallet and download the blockchains here because it will be faster without having any problem? I don't use Bitcoin Core at all Its just that my money is there and it was a long time ago. 
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