I have had good results with Nahema. You can get it at Roses Unlimited. It is hardy in zone 5.

Here is a link that might be useful: Delbard Roses at RU

Ramblin' Red is hardy in my z4 area left on the trellis with no winter protection. Also good disease resistance but has lots of thorns if that is an issue. Below is a good video on training your climbing rose.

Here is a link that might be useful: youtube video

Purple Splash, very fast grower, 12+' and very hardy. Looks nice with climbing iceberg (also very hardy), though iceberg takes longer to establish.

How far above the ground is your balcony? Will you be planting in the ground, or in pots?

These have all been hardy for me, so far, in 5a.

Parade, an iconic world famous climber from Beorner

Rosarium Uetersen non stop producer of raspberry-salmon pinkish, fully double blooms--I think the color is more salmon in brighter sun than I get in NY, from Kordes

Karlesruhe, a parent of the above, a darker pink, larger flower, not quite as rapid rebloom for me.

Dream Girl, lovely pink climber by Jacobus, available at Greenmantle.

Shin Setsu, white climber from Suzuki, excellent growth and vitality in a cold climate, why this has not remained in commerce I don't know

White Cocade, beautifully shaped soft white flowers..

In general, any of the climbers which have New Dawn for a parent, except possibly Casino and other yellows, are hardy to at least 5. New Dawn itself and sports are armoured and probably not good choices for placement near a hot tub.

Also any of the Kordesii climbers, such as the above mentioned, should work for you. Some newer ones which have amazingly beautiful flowers are Rosanna, Laguna, White Cloud.

Northland Rosarium has a nice selection of hardy climbers and their plants and service are excellent.

No personal experience but ran across this when checking the cold tolerance of some of my climbers.

William Baffin

Canadian Explorer roses were developed in Canada during a 30-year period from the 1960s through the 1990s. Bred to be cold-hardy, some are also drought-tolerant. One variety, "William Baffin" (Rosa "William Baffin"), climbs between 7 and 10 feet and bears semi-double pink flowers. It is hardy in USDA zones 2b through 9b, meaning that it can withstand winter temperatures as low as -45 degrees Fahrenheit and a significant number of days when temperatures are above 86 degrees Fahrenheit, as in south-central Florida's USDA zone 9b and American Horticultural Society Heat Zone 10 climate.
New Dawn

"New Dawn" (Rosa "New Dawn") is a vigorous climbing rose that grows between 15 and 20 feet tall, with a 15 foot spread. It is hardy in USDA zones 4b through 9a and can withstand winter temperatures as low as -25 degrees Fahrenheit. The large flowers are shell pink and are borne in profusion in spring and occasionally thereafter. "New Dawn" was selected as one of Texas A&M University's hardy, sustainable "Earth-Kind" roses after eight years of research and field trials in a variety of Texas locations. The field trial results recognize overall hardiness, as well as pest and disease resistance.