Switzerland had a bad time in the Great Depression. There's a bit of uncertainty about this, as Swiss National Accounts only started in 1948, so data is limited. But there's a bunch of indicators showing a significant drop in output and national income from 1929 to 1936, with recovery only coming in 1937. Swiss industrial production is estimated to have dropped 21% between 1929 and 1932, compared to a 46% drop in the USA and an 11% drop in the UK.

What's more, the Swiss production index took much longer to recover than the UK or German ones did, only reaching 1929 levels in 1937. 

So why did the Swiss economy take so long to recover? Normally I'm skeptical about attempts to explain the economic outcomes of an individual country at a particular time, but in the case of Switzerland in the Great Depression we can compare it with other European countries along an important axis: the gold standard. The gold standard is a system whereby the issuers of currency commit to redeeming each unit of currency for a fixed amount of gold, this was widely used in the 19th century and the early part of the 20th century, but fell apart during the 1930s.  A number of countries like the UK and the Scandinavians abandoned the gold standard early in the 1930s ('abandoned' here includes devaluing against it), and Spain was already off by the Great Depression. The USA devalued in 1933. Meanwhile, Switzerland meanwhile was part of the "Gold Bloc", along with Belgium, France, Netherlands, and Poland: they held onto the gold standard at the old rates for several more years, France and Switzerland not leaving until October 1936 (the last major countries to leave it).  

With the advantage of hindsight, it seems pretty clear that the Gold Bloc countries, including Switzerland, made the wrong decision: the countries that left earlier recovered more rapidly and more vigorously than the ones who left later. This has been shown not just in Europe, but also in Latin America, and despite quite similar macroeconomic conditions in 1929 and 1932 between those countries which stayed and those which left. Countries who abandoned the gold standard could expand the domestic money supply, stopping the large deflation seen from 1929 to 1931 (in all the countries with reasonable statistics). This sort of deflation is bad because it makes it hard for borrowers to repay debts and it encourages consumers to delay purchases as they expect lower prices in the future. 

Switzerland did have one advantage over other countries on the gold standard, the Swiss central bank had large gold reserves and thus didn't need to significantly raise Swiss interest rates to stay on gold. For example, in May 1935, the Swiss central bank raised its discount rate to 2.5% for a period, France had to push it up to 6% for times to defend the gold standard. 

Along with staying on the gold standard, Switzerland engaged in considerable intervention in the domestic economy to protect relevant political interest groups. For example, there was cartelisation of the watch-making industry, a ban on hotel construction, and on opening or extending department stores, and purchase guarantees for agricultural products to maintain prices. This impeded internal adjustment to changing prices, contributing to the longer recession. 

Swiss banks were also hurt, as growing numbers of customers experienced financial difficulties. Banks also had to take write-offs against their assets as Germany freezed its credit balances in 1931 and introduced controls on capital and a number of Central and Eastern European countries followed suit. This meant that, while banks might have had assets on paper, many of them were trading at a sharp discount. 

As for Keynesian policies, this is typically taken to mean the government running significant deficits when the economy contracts. Switzerland didn't pursue counter-fiscal policies. Swiss central and local governments increased public spending during the Depression but funded that mainly via taxes. Total budget deficits in Switzerland never exceeded 1.2% of net national product. This, incidentally, was generally true of Western countries during this time, for example the New Deal funding in the USA was mainly funded by taxes: there were US deficits but these are mainly considered vastly insufficient (within a Keynesian framework) for the size of the Great Depression. There's some evidence that the Netherlands and Sweden had some counter-cyclical fiscal policies, but of a relatively small size. Generally, Keynes' influence on economic policy making was strongest after WWII. (Note there is some debate about this, there's significant data limitations for this time period). 

Sources

 Peter Rosenkranz, Tobias Straumann and Ulrich Woitek, A Small Open Economy in the Great Depression: the Case of Switzerland, Working Paper No. 164, University of Zurich, 2014, https://www.econ.uzh.ch/static/release/workingpapers.php?id=841

Mathias Zurlinden, Gold Standard, Deflation and Depression: The Swiss Economy during the Great Depression, Swiss National Bank Quarterly Bulletin, 2/2003, https://www.snb.ch/en/mmr/reference/quartbul_2003_2/source/quartbul_2003_2.en.pdf

Bernanke, Ben S. “The Macroeconomics of the Great Depression: A Comparative Approach.” Journal of Money, Credit, and Banking 27 (1995): 1-28. https://fraser.stlouisfed.org/title/1169/item/2399

Price Fishback, US monetary and fiscal policy in the 1930s, Oxford Review of Economic Policy, Volume 26, Issue 3, Autumn 2010, Pages 385–413, https://doi.org/10.1093/oxrep/grq029

Kavonius, Ilja Kristian, 2010. Fiscal policies in Europe and the United States during the Great Depression, Working Papers 13, VATT Institute for Economic Research.  https://ideas.repec.org/p/fer/wpaper/13.html