The 6.5X57mm is very close to the 6.5X55mm Mauser in 'internal ballistics' terms (ie the metrics that determine the pressures and MVs cartridges produce with any given barrel length and bullet weight).
They also operate at equivalent pressures, CIP MAP for the modern (SE) 6.5X55 at 55,114 psi; 56,565 psi for the 6.5X57mm, so the latter is in no way peak-pressure constrained in any comparison. (This assumes your 6.5X57mm rifle uses a modern or otherwise strong older action such as the M98 Mauser in good condition. As many German and Austrian 6.5X57s were built around the older, weaker M93/95 action, such historic pieces should be restricted to Swedish military Mauser pressures, ie around 45,000 psi. It also assumes your rifle is bolt-action using the rimless version of the cartridge not the 6.5X57R rim version that is rated at lower maximum pressures.)
Where there is modest divergence is in case capacity (measured in water in grains weight) in that the 57mm case variant is listed in QuickLOAD as 59gn water compared to the Swede's 57gn. So, the German model runs with a slightly larger combustion chamber volume behind the same bullets going down the same bore. This
reduces pressures slightly compared to the 6.5X55 when combining the same powders, charges and bullets - ie it is a 'right-side (safe) change as it lowers pressures not the reverse. Running a 120gn Nosler BT load in QuickLOAD with various powders confirms that with same weight charges showing 1,000-1,500 psi lower pressure in the 6.5X57mm.
Of the powders you list, N133 is unsuitable being too fast burning and N140 is marginal especially in still larger case than that of the 6.5X55mm. Of N150 and N160, I'd lean toward the latter as a very much better match that will give a 90% + case fill with full working loads. In fact, I'd prefer something a tad slower burning.
Hornady lists the 6.5X57 in its reloading manuals, but it is old data and only uses three Reach non-compliant US powders - IMR-4064 / 4350 / 4831. It didn't test the cartridge with any 120gn bullets (actually didn't make any back when it worked up the data for this cartridge) so the nearest equivalent is the 129gn SST. Comparing the IMR-4350 maximum loads for this bullet with those in the same company's table for the 6.5X55 again shows that the 6.5X57mm allowed maximum is slightly higher than the 6.5X55's so the latter will be usable and should be safe as producing slightly lower pressures. The same relationship applies to the two cartridges in Hornady's 140gn bullet table, here for IMR-4831.
There will be data around online for the 6.5X57 I'm sure, most likely on German hunters' sites and forums. There is one here for Ballistix Bullets, a South African custom bullet manufacturer. Again, it's not the actual loads that matter, but the colmparison it allows between 6.5X57 and 6.5X55 recommendations, the same pattern applying of the same powders being used, but with marginally heavier maximum loads for the German cartridge demontrating the suitability of starting with readily available 6.5X55mm Viht data.
Vihtavuori - Balistix Bullets
I'm sorry to look so long-winded on this, but on those occasions where extrapolation between cartridge's data is attempted, serious research and justification is needed to be safe. Put all of the above factors together and I personally would be happy to use published 6.5X55 loads. Usually, extrapolating loads from one cartridge to another is an unwise and potentially very dangerous practice, not at all recommended as Apthorpe says in his post, but it is safe and allowable in a few cases such as this where the two have very similar characteristics. (Another widely used example for a European cartridge is the 7X64 Brennecke which is very close internally to the 280 Remington and whose much more widely available loading data can be used with a small reduction in maximum charges purely for insurance.)
So use Viht's loads tables on its website for the 6.5X55 (lower pressure 'Swedish Mauser' not the higher pressure 'SKAN' table initially) for the 120gn Lapua Scenar L which will be close enough to your Nosler bullet to be safe. It lists 43.8gn starting and 45.7gn maximum of N160.
This compares to Nosler's load for the 6.5X55 for the 120gn Ballistic Tip in the company's No.6 Reloading Manual of 42.5gn starting / 46.5gn maximum N160 (for modern strong action rifles in good condition) so ties in OK.
Ideally results should be checked out on a chronograph to ensure they're in lone with expectations - ie slightly reduced MVs.
In most circumstances I'd have recommended requesting a QuickLOAD user to model the bullet / powder combination for you, would have done so myself. However, I won't trust the program with Viht N160 - it undercalculates pressures by ~5,000 psi IME and I've blown a primer or two and wrecked the odd case finding this out the hard way over the years. So, for other forum members who will no doubt be inserting copies of N160 runs for the 6.5X57 for you in a spirit of helpfulness, please don't!