You are asking about using the whole DNA pol I, not the Klenow fragment?  

I could be wrong, but wouldn't it be the same protocol as Klenow, right?  Klenow is just pol I with the domain for 5'-3' exonuclease activity removed, which should not matter for filling 5'-overhangs (since that is only type of end it will fill).

https://www.neb.com/applications/dna-modification/dna-end-modification/dna-blunting

There's also T4 DNA Polymerase which will blunt by trimming 3' overhangs and filling-in 3' recessed ends.

https://www.neb.com/protocols/2014/01/13/protocol-for-blunting-ends-by-3-overhang-removal-and-fill-in-of-3-recessed-5-overhang-ends-using1

I used to construct vector (always had to change very specific nt). We chose the combination of Klenow with specific dNTG and/or Mung Bean Nucleas. In this way you can manipulate the sticky ends quite easily.

Hi there,

If your sticky ends are 5' overhangs, you can do it thanks to the 5' to 3' polymerase activity of polI . If 3' overhang, polI is not the ideal enzyme because its 3' to 5' exonuclease activity is not specific enough to ensure the generation of blunt ends only...

Has anyone experience using a conventional proofreading DNA polymerase, such as the NEB phusion? And in case suggestion for a protocol?