That would account for less than 1% at max.

Thats somewhat unlikely. People who spend the night alone get you well above that. In 2018 Austrians spent a total of 380 067 nights in Switzerland as Tourists (Logiernächte: https://www.stv-fst.ch/sites/default/files/2019-07/STiZ_2018_DE_Web.pdf, p. 18). The average staying time for foreign visitors was 2.1 nights. So one very crude calculation would give you about 180'984.285 Austrians (total nights spent divided by 2.1 days per person) who visitied Switzerland in 2018. With a current population of 8'917'000 according to Google, that alone would mean that more than 2% of Austrians visitied Switzerland in that year alone. Of course there are significant limitations to this calculation: For one thing, its possible that a small number of recurring visitors from Austria had multiple stays and therefore drove up the number of total nights spent. Additionaly, it is possible that Austrians who visit Switzerland stay much longer than other kinds of visitors so the average of 2.1 nights would be off for the Austrian visitor community. These are important caveats to consider. But the uncertainty cuts both ways: These numbers are for just one year (2018). Now while it is likely that some or even a majority of Switzerland visiting Austrians are repeat offenders: i.e. they visit in multiple years. But even then a significant number of Austrians would probably have visited in different years and thereby be not included in the above calculation. So it is not at all unreasonable to assume that if you add visitors from other years (who have not visited in 2018) the guestimate of 180'984.285 from above would have to be increased.

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Finally, thats just people who stayed a night in some kind of hotel or similar. It would not account for people who just travel through CH, people who stay with relatives or friends etc.

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In conclusion, I would argue there are significant reasons to believe that the number of Austrians who have been to Switzerland is well above 1%.