Listen to the interview again.
Following "free agent frenzy" in the first few days of July, most teams will have addressed their 2017-2018 roster concerns.
http://www.tsn.ca/mcphee-vegas-will-build-through-entry-draft-1.764973
Direct quote from that interview between McPhee & Lebrun.
"We can't keep 30 players because we can't get six or seven players through waivers if we wanted to, most of them are not waiver exempt. We'll do the best we can and
I would say there will probably be a lot of transactions between the day we announce the picks (on June 21) and the entry draft (on June 23), because you know in this business,
you have to move players quickly and make your changes quickly because once you get into July 5, there's not a lot of liquidity in the market, people have made their decisions and you don't want to get stuck holding the bag."
Also relevant that McPhee offers up this information without being questioned about it. It's obviously at the forefront of his mind.
Although "picks for players" is one avenue Mcphee will want done before the entry draft, he'll also be trading "prospects for players." He'll have an easier time at the draft table once he has some semblance of knowing what he has in his organization. It's quite likely these deals will happen quickly.
Further although McPhee will have "months" to worry about waivers, the point he made in his interview was that his option would become limited once the first few days of free agency were over & finding takers for his overflow would become more difficult.
Major deals are imminent.