I have had great results with Nice Shot in my Damascus barreled guns. Rather than risk using Heavy Shot I would use either Nice Shot or large Bismuth as Scott suggested.
To start, "choke" is the measure of performance not the constriction that causes. Example, a gun that shoots 70% of the pellets in a 30" circle at 40 yards delivers full choke patterns. That gun might have a barrel constriction of .025" or .045" depending on the shot size, shot hardness, velocity, or shape of the constriction. I'll use choke constriction rather than the erroneous term choke.
A choke constriction creates a venturi effect so that the shot squirts out of the muzzle. It is just like water leaving a garden hose.
Lead shot does compress a little but more so flows out of the constriction. The shot at the front is accelerated so that it is traveling faster than it was prior to being constricted. The very last pellets to leave the barrel were not squirted out at a velocity faster that they had when before entering the constricted area. This is why the shot string is longer for a full choke than the same load from a more open choke constriction.
Large round shot be it lead or steel doesn't flow through a choke constriction as easily as does smaller round shot. Shot buffer helps lubricate this flow. Heavy Shot being irregular shapes doesn't flow well at all.
Tom Rooster patented thick and plastic harder shot cup wads so that the second generation of steel shot could be used in tighter choke constrictions.
The wads in factory Heavy Shot loads are at least twice as thick at their thinnest area in their petals as the modern full choke constrictions. This gives the pellets a soft cushion it compress into should they not be able to flow via the venturi effect. One should cut open modern Heavy Shot and steel shot shells and study the wads used.
WARNING: The following is only for Damascus barrels that are in as new condition. They should be accurately measured for minimum barrel wall thickness radially. This inspection should be preformed by a qualified doublegun smith.
The following is not for a Belgian clunker, hardware store gun, of other piece of crap although they might be perfect test subjects... 
Restrict this to Parkers, LC Smiths, Bakers, and other guns whose names have become legends.
If I desired to shoot Heavy Shot rather than Nice Shot I would do the following:
1. Use unslit wads made for steel shot as Holeshot suggested.
2. Add a mylar liner for extra cushion thickness.
3. Ensure that the total thickness of the wad petals is at least twice that of my choke constriction, i.e. .040" choke constriction being .020" at any radial of the barrel requires a wad petal of at least .040". I might start with total petal thickness that is three times the thickness of the constriction.
4. Use shot buffer made for Heavy Shot.
5. Ensure that the shot column is lower that the shot cup. Remember when the shot column is compressed it will increase in height.
6. Start with no larger than #4 Heavy Shot. Find the wads after shooting such as when you pattern your load. Examine those wads for how far the pellets compressed the plastic in the petals.
I once hunted with someone who shot Federal factory loaded steel shot through a #2 frame Parker with Damascus barrels which had .035 and ,040" choke constrictions. After 200 rounds that gun had no problems other than the stock.
Oh, when I got caught short of shell as a flock was coming in. That same someone handed me a half dozen steel shot loads which I shot in my #2 frame Parker with no bad results.
Damascus, the original nano technology is more elastic than fluid steel. I believe that if all else were the same such as bore size and choke constriction and shape, that the same load of lead or steel shot would cause the Damascus barrel to expand more than would the barrel of fluid steel. The is Young's Modulas in that everything is a spring.
PS: Only shoot steel or Heavy Shot through barrels that you can afford to lose! The old wives tales of the horrors of both Damascus and steel shot may come true...
Consider using Bismuth or Nice Shot
Mark