Solid axles are strong and I've found that a mere 4" adjustable wrench is all that is needed to secure the axle nuts if the threads are kept well-oiled.

Some 4" adj wrenches need to be filed out to the 15mm of most axle nuts (or 16mm, 5/8" on a Schwinn Varsity, lol).

Using modern 8s chain, I find that I can go as low as 3.3mm clearance out from the face of the smallest cog to the outer face of the axle locknut. This is a huge(!) reduction from what many vintage 5s or 6s hubs had, and which was just redundant space that the chain could literally fall into.

So, with many 5s/120mm hubs, a standard 6s freewheel may give running clearance for the chain with just a thin washer added to the driveside. This is what I have done many times, although Campagnolo hubs have less redundant extra axle length since they weren't designed to cope with inward-protruding axle-locating stops or claw hangers.

Lastly, the design of the frame's seatstay may interfere with the chain if larger smallest cog size is used. 12t and 13t smallest cogs give much better chain clearance on those frames that are poorly designed in this area.

As far as wheel strength, it's ok to add a small bit of dish as part of the already-needed equi-tensioning process, and the wheel usually ends up stronger.

Any Shimano 7s freehub can have a 1mm washer removed from each end of it's axle assembly and still provide plenty of running clearance for the chain, this requiring no re-dish at all and ending up with only 124mm over-locknut width.