It’s true that majority of Scandinavia has only Scandinavized very late, only at the second millennium AD. And now (since 2004) we also know that there truly was a Palaeo-European substrate language (or even more of them) in northern Scandinavia. This language, however, seems to have had nothing in common with the Uralic, Finnic or Baltic languages (or Basque, or Sumerian, etc.).
What comes to the claim of Elert, that “On archeological, genetic and linguistic grounds the late Bronze Age language in Scandinavia could have been a Finnic or Baltic language (or both)”, this claim is just based on the invalid method, in which one assumes that archaeological or genetic continuity could testify for linguistic continuity, too. But this is a false assumption, and the invalidness of this method has been presented here:
http://www.mv.helsinki.fi/home/jphakkin/Uralic.html
Or in Finnish:
http://www.tieteessatapahtuu.fi/0106/hakkinen.pdf
So, what is the true linguistic evidence for the earlier Finnic or Baltic presence in Scandinavia? None. There is neither loanword stratum, nor place-name stratum from these languages in Scandinavia(n). Zero evidence. Nought. Nil. Saamic loanwords and place-names there are, of course, but they cannot predate the Proto-Saamic development which occurred in Southern Finland only 2 000 years ago. So, even the Saamic languages were not there during the Bronze Age, even though it was earlier thought so (based on the above-mentioned erroneous method).
http://www.mv.helsinki.fi/home/jphakkin/Jatkuvuus2.pdf