You really don't need a bee vac to do a proper removal but they sure do make life a lot easier. The key to success with most all removals is transferring and securing brood comb to the new set up and removing all comb from the void space. You need some bees covering what comb was transferred so they don't get chilled unless it is very warm out. If no bee vac nor bee quick or honey robber use your smoker to herd the bees where you need them to go. Don't push the bees too much but be aggressive when herding them. Pay attention to their movement. If they are going, let them, if hung up edge them until they move again. Uncertain, step back & give them time to determine their motives.
If they aren't stingy you can use your hands or cardboard whatever works.
On one like this with a lack of tools I would leave the set up on site & do periodic inventory checks. I've left set ups before when I hadn't caught the queen during the removal to have her and the rest of the bees wind up in the set up, albeit it may take a day or two achieve results.
There is always the dreaded chance that they will not be interested in the set up but in my experience this is not the norm.
Best of luck man & keep us updated!